Multiparameter quantum Schur duality of type B
Huanchen Bao, Weiqiang Wang, and Hideya Watanabe
TL;DR
This paper establishes a new duality between a coideal subalgebra of quantum type A and type B Hecke algebra, linking their canonical bases and advancing understanding of quantum symmetries.
Contribution
It introduces a Schur duality of type B involving a coideal subalgebra and two-parameter Hecke algebra, connecting canonical bases in a novel way.
Findings
Identifies the $ extit{ extbf{}}$-canonical basis with Lusztig's canonical basis
Establishes a Schur duality between quantum type A coideal subalgebra and type B Hecke algebra
Links bases in tensor products to dual algebraic structures
Abstract
We establish a Schur type duality between a coideal subalgebra of the quantum group of type A and the Hecke algebra of type B with 2 parameters. We identify the -canonical basis on the tensor product of the natural representation with Lusztig's canonical basis of the type B Hecke algebra with unequal parameters associated to a weight function.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Algebra and Geometry