We introduce the doubled Hecke algebra, which is an infinite-dimensional algebra generated by two Hecke algebras. This concept originates from the degenerate doubled Hecke algebra in the theory of Schur-Weyl duality related to enhanced reductive algebraic groups. We study the finite-dimensional natural representation of the doubled Hecke algebra on tensor space and prove that the doubled Hecke algebra forms a duality with the quantum group of Levi type.
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Xue et al. (2024) studied this question.
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