Canonical bases of $q$-Brauer algebras and $\imath$Schur dualities
Weideng Cui, Yaolong Shen
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Abstract
Expanding the classical work of Kazhdan-Lusztig, we construct a bar involution and canonical bases on the -Brauer algebra introduced by Wenzl. We define explicit actions of the -Brauer algebra on the tensor spaces, and formulate Schur dualities between the -Brauer algebra and the quantum groups of type AI and AII respectively.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Advanced Topics in Algebra