Adriano Moura
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Adriano Moura has a total of 39 co-authors. Here are the top co-authors by number of shared publications:
- Vyjayanthi Chari
Department of Mathematics, University of California, Riverside, USA
7 shared publications Dijana Jakelić
University of North Carolina at Wilmington, Wilmington, NC
5 shared publications- Vyjayanthi Chari
University of California
5 shared publications Clayton Silva
4 shared publications- Matheus Brito
Departamento de Matemática, UFPR, Curitiba, Brazil
4 shared publications - Angelo Bianchi
UNIFESP -ICT São José dos Campos -SP 12231-280 -Brazil
3 shared publications
Latest Publications
- Open Access
- 3 March 2026
- Published by Springer Nature in Algebras and Representation Theory
- Vol. 29 (2) , 443-493
Imaginary Modules Arising from Tensor Products of Snake Modules
Motivated by the limitations of cluster algebra techniques in detecting imaginary modules, we build on the representation-theoretic framework developed by the first author and Chari to extend the construction of such modules beyond previously known cases, which arise from the tensor product of a higher-order Kirillov–Reshetikhin module and its dual. Our first main result gives an explicit description of the socle of tensor products of two snake modules, assuming the corresponding snakes form a covering pair of ladders. By considering a higher-order generalization of the covering relation, we describe a sequence of inclusions of highest- $$\ell $$ -weight submodules of such tensor products. We conjecture all the quotients of subsequent modules in this chain of inclusions are simple and imaginary, except for the socle itself, which might be real. We prove the first such quotient is indeed simple and, assuming an extra mild condition, we also prove it is imaginary, thus giving rise to new classes of imaginary modules within the category of finite-dimensional representations of quantum loop algebras in type A .- 3 March 2026
- Published by Springer Nature in Algebras and Representation Theory
- Vol. 29 (2) , 443-493
Open AccessImaginary Modules Arising from Tensor Products of Snake Modules
Motivated by the limitations of cluster algebra techniques in detecting imaginary modules, we build on the representation-theoretic framework developed by the first author and Chari to extend the construction of such modules beyond previously known cases, which arise from the tensor product of a higher-order Kirillov–Reshetikhin module and its dual. Our first main result gives an explicit description of the socle of tensor products of two snake modules, assuming the corresponding snakes form a covering pair of ladders. By considering a higher-order generalization of the covering relation, we describe a sequence of inclusions of highest- $$\ell $$ -weight submodules of such tensor products. We conjecture all the quotients of subsequent modules in this chain of inclusions are simple and imaginary, except for the socle itself, which might be real. We prove the first such quotient is indeed simple and, assuming an extra mild condition, we also prove it is imaginary, thus giving rise to new classes of imaginary modules within the category of finite-dimensional representations of quantum loop algebras in type A . - 10 October 2025
- Published by Elsevier in Journal of Algebra
- Vol. 688, 244-283
Reality determining subgraphs and strongly real modules
- 10 October 2025
- Published by Elsevier in Journal of Algebra
- Vol. 688, 244-283
Reality determining subgraphs and strongly real modules
- Open Access
Tensor Product Decompositions, Limits in Excellent Filtrations, Affine Weyl Group Orbits, and Tableaux Counting
We express the outer multiplicities in the tensor products of two fundamental simple modules for an affine Kac-Moody algebra of type $A$ in terms of counting certain sets of multipartitions by exploring the stabilizing limits of certain excellent filtrations. This extends for all ranks a previously obtained result by Jakelić and the second author for rank $1$. The same outer multiplicities were previously computed by Misra and Wilson in terms of counting certain sets of tableaux. By comparing these two expressions and by explicitly exhibiting a combinatorial description of level-$2$ affine Weyl group orbits, we establish the existence of a bijection between the Misra-Wilson set of tableaux and a disjoint union of certain sets of multipartitions.Open AccessTensor Product Decompositions, Limits in Excellent Filtrations, Affine Weyl Group Orbits, and Tableaux Counting
We express the outer multiplicities in the tensor products of two fundamental simple modules for an affine Kac-Moody algebra of type $A$ in terms of counting certain sets of multipartitions by exploring the stabilizing limits of certain excellent filtrations. This extends for all ranks a previously obtained result by Jakelić and the second author for rank $1$. The same outer multiplicities were previously computed by Misra and Wilson in terms of counting certain sets of tableaux. By comparing these two expressions and by explicitly exhibiting a combinatorial description of level-$2$ affine Weyl group orbits, we establish the existence of a bijection between the Misra-Wilson set of tableaux and a disjoint union of certain sets of multipartitions. - Open Access
Imaginary modules arising from tensor products of snake modules
Motivated by the limitations of cluster algebra techniques in detecting imaginary modules, we build on the representation-theoretic framework developed by the first author and Chari to extend the construction of such modules beyond previously known cases, which arise from the tensor product of a higher-order Kirillov--Reshetikhin module and its dual. Our first main result gives an explicit description of the socle of tensor products of two snake modules, assuming the corresponding snakes form a covering pair of ladders. By considering a higher-order generalization of the covering relation, we describe a sequence of inclusions of highest-$\ell$-weight submodules of such tensor products. We conjecture all the quotients of subsequent modules in this chain of inclusions are simple and imaginary, except for the socle itself, which might be real. We prove the first such quotient is indeed simple and, assuming an extra mild condition, we also prove it is imaginary, thus giving rise to new classes of imaginary modules within the category of finite-dimensional representations of quantum loop algebras in type A.
Open AccessImaginary modules arising from tensor products of snake modules
Motivated by the limitations of cluster algebra techniques in detecting imaginary modules, we build on the representation-theoretic framework developed by the first author and Chari to extend the construction of such modules beyond previously known cases, which arise from the tensor product of a higher-order Kirillov--Reshetikhin module and its dual. Our first main result gives an explicit description of the socle of tensor products of two snake modules, assuming the corresponding snakes form a covering pair of ladders. By considering a higher-order generalization of the covering relation, we describe a sequence of inclusions of highest-$\ell$-weight submodules of such tensor products. We conjecture all the quotients of subsequent modules in this chain of inclusions are simple and imaginary, except for the socle itself, which might be real. We prove the first such quotient is indeed simple and, assuming an extra mild condition, we also prove it is imaginary, thus giving rise to new classes of imaginary modules within the category of finite-dimensional representations of quantum loop algebras in type A.
- Open Access
Totally ordered pseudo q-factorization graphs and prime factorization
In an earlier publication, the last two authors showed that a finite-dimensional module for a quantum affine algebra of type $A$ whose $q$-factorization graph is totally ordered is prime. In this paper, we continue the investigation of the role of totally ordered pseudo $q$-factorization graphs in the study of the monoidal structure of the underlying abelian category. We introduce the notions of modules with (prime) snake support and of maximal totally ordered subgraphs decompositions. Our main result shows that modules with snake support have unique such decomposition and that it determines the corresponding prime factorization. Along the way, we also prove that prime snake modules (for type $A$) can be characterized as the modules for which every pseudo $q$-factorization graph is totally ordered.Open AccessTotally ordered pseudo q-factorization graphs and prime factorization
In an earlier publication, the last two authors showed that a finite-dimensional module for a quantum affine algebra of type $A$ whose $q$-factorization graph is totally ordered is prime. In this paper, we continue the investigation of the role of totally ordered pseudo $q$-factorization graphs in the study of the monoidal structure of the underlying abelian category. We introduce the notions of modules with (prime) snake support and of maximal totally ordered subgraphs decompositions. Our main result shows that modules with snake support have unique such decomposition and that it determines the corresponding prime factorization. Along the way, we also prove that prime snake modules (for type $A$) can be characterized as the modules for which every pseudo $q$-factorization graph is totally ordered. - 7 April 2023
- Published by Taylor & Francis in Communications in Algebra
- Vol. 51 (9) , 4054-4090
Three-vertex prime graphs and reality of trees
We continue the study of prime simple modules for quantum affine algebras from the perspective of q-fatorization graphs. In this paper we establish several properties related to simple modules whose q-factorization graphs are afforded by trees. The two most important of them are proved for type A. The first completes the classification of the prime simple modules with three q-factors by giving a precise criterion for the primality of a 3-vertex line which is not totally ordered. Using a very special case of this criterion, we then show that a simple module whose q-factorization graph is afforded by an arbitrary tree is real. Indeed, the proof of the latter works for all types, provided the aforementioned special case is settled in general.
- 7 April 2023
- Published by Taylor & Francis in Communications in Algebra
- Vol. 51 (9) , 4054-4090
Three-vertex prime graphs and reality of trees
We continue the study of prime simple modules for quantum affine algebras from the perspective of q-fatorization graphs. In this paper we establish several properties related to simple modules whose q-factorization graphs are afforded by trees. The two most important of them are proved for type A. The first completes the classification of the prime simple modules with three q-factors by giving a precise criterion for the primality of a 3-vertex line which is not totally ordered. Using a very special case of this criterion, we then show that a simple module whose q-factorization graph is afforded by an arbitrary tree is real. Indeed, the proof of the latter works for all types, provided the aforementioned special case is settled in general.
- 20 March 2023
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 76 (2) , 594-637
On the primality of totally ordered q-factorization graphs
We introduce the combinatorial notion of a q-factorization graph intended as a tool to study and express results related to the classification of prime simple modules for quantum affine algebras. These are directed graphs equipped with three decorations: a coloring and a weight map on vertices, and an exponent map on arrows (the exponent map can be seen as a weight map on arrows). Such graphs do not contain oriented cycles and, hence, the set of arrows induces a partial order on the set of vertices. In this first paper on the topic, beside setting the theoretical base of the concept, we establish several criteria for deciding whether or not a tensor product of two simple modules is a highest- $\ell $ -weight module and use such criteria to prove, for type A, that a simple module whose q-factorization graph has a totally ordered vertex set is prime.- 20 March 2023
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 76 (2) , 594-637
On the primality of totally ordered q-factorization graphs
We introduce the combinatorial notion of a q-factorization graph intended as a tool to study and express results related to the classification of prime simple modules for quantum affine algebras. These are directed graphs equipped with three decorations: a coloring and a weight map on vertices, and an exponent map on arrows (the exponent map can be seen as a weight map on arrows). Such graphs do not contain oriented cycles and, hence, the set of arrows induces a partial order on the set of vertices. In this first paper on the topic, beside setting the theoretical base of the concept, we establish several criteria for deciding whether or not a tensor product of two simple modules is a highest- $\ell $ -weight module and use such criteria to prove, for type A, that a simple module whose q-factorization graph has a totally ordered vertex set is prime.- Open Access
Three-vertex prime graphs and reality of trees
We continue the study of prime simple modules for quantum affine algebras from the perspective of $q$-fatorization graphs. In this paper we establish several properties related to simple modules whose $q$-factorization graphs are afforded by trees. The two most important of them are proved for type $A$. The first completes the classification of the prime simple modules with three $q$-factors by giving a precise criterion for the primality of a $3$-vertex line which is not totally ordered. Using a very special case of this criterion, we then show that a simple module whose $q$-factorization graph is afforded by an arbitrary tree is real. Indeed, the proof of the latter works for all types, provided the aforementioned special case is settled in general.Open AccessThree-vertex prime graphs and reality of trees
We continue the study of prime simple modules for quantum affine algebras from the perspective of $q$-fatorization graphs. In this paper we establish several properties related to simple modules whose $q$-factorization graphs are afforded by trees. The two most important of them are proved for type $A$. The first completes the classification of the prime simple modules with three $q$-factors by giving a precise criterion for the primality of a $3$-vertex line which is not totally ordered. Using a very special case of this criterion, we then show that a simple module whose $q$-factorization graph is afforded by an arbitrary tree is real. Indeed, the proof of the latter works for all types, provided the aforementioned special case is settled in general. - 17 January 2019
- Published by Taylor & Francis in Communications in Algebra
- Vol. 47 (3) , 1125-1146
On truncated Weyl modules
We study structural properties of truncated Weyl modules. A truncated Weyl module is a local Weyl module for , where is a finite-dimensional simple Lie algebra. It has been conjectured that, if N is sufficiently small with respect to λ, the truncated Weyl module is isomorphic to a fusion product of certain irreducible modules. Our main result proves this conjecture when λ is a multiple of certain fundamental weights, including all minuscule ones for simply laced . We also take a further step towards proving the conjecture for all multiples of fundamental weights by proving that the corresponding truncated Weyl module is isomorphic to a natural quotient of a fusion product of Kirillov–Reshetikhin modules. One important part of the proof of the main result shows that any truncated Weyl module is isomorphic to a Chari–Venkatesh module and explicitly describes the corresponding family of partitions. This leads to further results in the case that related to Demazure flags and chains of inclusions of truncated Weyl modules.- 17 January 2019
- Published by Taylor & Francis in Communications in Algebra
- Vol. 47 (3) , 1125-1146
On truncated Weyl modules
We study structural properties of truncated Weyl modules. A truncated Weyl module is a local Weyl module for , where is a finite-dimensional simple Lie algebra. It has been conjectured that, if N is sufficiently small with respect to λ, the truncated Weyl module is isomorphic to a fusion product of certain irreducible modules. Our main result proves this conjecture when λ is a multiple of certain fundamental weights, including all minuscule ones for simply laced . We also take a further step towards proving the conjecture for all multiples of fundamental weights by proving that the corresponding truncated Weyl module is isomorphic to a natural quotient of a fusion product of Kirillov–Reshetikhin modules. One important part of the proof of the main result shows that any truncated Weyl module is isomorphic to a Chari–Venkatesh module and explicitly describes the corresponding family of partitions. This leads to further results in the case that related to Demazure flags and chains of inclusions of truncated Weyl modules.- 7 October 2018
- Published by Mathematical Sciences Publishers in Pacific Journal of Mathematics
- Vol. 297 (1) , 147-193
Non-minimality of certain irregular coherent preminimal affinizations
- 7 October 2018
- Published by Mathematical Sciences Publishers in Pacific Journal of Mathematics
- Vol. 297 (1) , 147-193
Non-minimality of certain irregular coherent preminimal affinizations