On crystal bases of two-parameter (v,t)(v, t)-quantum groups

preprint2014arXivOpen access

Abstract

Following Kashiwara's algebraic approach in one-parameter case, we construct crystal bases for two-parameter quantum algebras and for their integrable modules. We also show that the global crystal basis coincides with the canonical basis geometrically constructed by Fan and Li up to a 2-cocycle deformation.

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