Two-parameter quantum algebras, canonical bases and categorifications
Representation Theory
2013-11-06 v2 Quantum Algebra
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. 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 analogue.
Cite
@article{arxiv.1303.2429,
title = {Two-parameter quantum algebras, canonical bases and categorifications},
author = {Zhaobing Fan and Yiqiang Li},
journal= {arXiv preprint arXiv:1303.2429},
year = {2013}
}
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