Two-Parameter Quantum Algebras, Canonical Bases, and Categorifications
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- 22 September 2014
- journal article
- Published by Oxford University Press (OUP) in International Mathematics Research Notices
- Vol. 2015 (16) , 7016-7062
Abstract
A theory of canonical basis for a two-parameter quantum algebra is developed in parallel with the one in one-parameter case. A geometric construction of the negative part of a two-parameter quantum algebra is given by using mixed perverse sheaves and Deligne's weight theory based on Lusztig's work [28]. A categorification of the negative part of a two-parameter quantum algebra is provided. A two-parameter quantum algebra is shown to be a two-cocycle deformation, depending only on the second parameter, of its one-parameter analog.Keywords
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