Unipotent Hecke algebras of GL_n(F_q)

Details Unipotent Hecke algebras of GL_n(F_q) Unipotent Hecke algebras of GL_n(F_q)

2004-02-24

arxiv.org/abs/math/0402383v1

Mathematics

Combinatorics

21 pages

Scientific paper

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

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