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Unipotent Hecke algebras of GL_n(F_q)

N. Thiem
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Abstract

This paper describes a family of Hecke algebras H_μ=End_G(Ind_U^G(ψ_μ)), where U is the subgroup of unipotent upper-triangular matrices of G=GL_n(F_q) and ψ_μis a linear character of U. The main results combinatorially index a basis of H_μ, provide a large commutative subalgebra of H_μ, and after describing the combinatorics associated with the representation theory of H_μ, generalize the RSK correspondence that is typically found in the representation theory of the symmetric group.

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N. Thiem. 2004-02-24. Unipotent Hecke algebras of GL_n(F_q). https://arxiv.org/abs/math/0402383

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