Symplectic Grassmannians and cyclic quivers

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Abstract
The goal of this paper is to extend the quiver Grassmannian description of certain degenerations of Grassmann varieties to the symplectic case. We introduce a symplectic version of quiver Grassmannians studied in our previous papers and prove a number of results on these projective algebraic varieties. First, we construct a cellular decomposition of the symplectic quiver Grassmannians in question and develop combinatorics needed to compute Euler characteristics and Poincaré polynomials. Second, we show that the number of irreducible components of our varieties coincides with the Euler characteristic of the classical symplectic Grassmannians. Third, we describe the automorphism groups of the underlying symplectic quiver representations and show that the cells are the orbits of this group. Lastly, we provide an embedding into the affine flag varieties for the affine symplectic group.
Funding Information
  • Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni
  • Ministero dell’Università e della Ricerca (CUP E83C18000100006, CUP E53D23005550006)
  • Deutsche Forschungsgemeinschaft (SFB-TRR 358/1 2023 – 491392403)
  • Università degli Studi di Roma La Sapienza

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