Duplex Hecke Algebras and Related Quantum Schur Duality
Chenliang Xue, An Zhang
TL;DR
This paper introduces the duplex Hecke algebra, an infinite dimensional algebra generated by two Hecke algebras, and establishes its duality with Levi type quantum groups through representation theory.
Contribution
It defines the duplex Hecke algebra and proves its duality with Levi type quantum groups, extending Schur-Weyl duality concepts.
Findings
Duplex Hecke algebra is an infinite dimensional algebra.
Establishes duality with Levi type quantum groups.
Provides finite dimensional natural representation on tensor space.
Abstract
This article introduces the duplex Hecke algebra, which is an infinite dimensional algebra generated by two Hecke algebras. This concept originates from the degenerate duplex Hecke algebra in the theory of Schur-Weyl duality related to enhanced reductive algebraic groups. We will study the finite dimensional natural representation of the duplex Hecke algebra on tensor space and prove that the duplex Hecke algebra forms a duality with the Levi type quantum group.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Algebra and Geometry