Iwahori component of the Gelfand--Graev representation for reductive groups

2026/07/19 by Yi Luo · 1 citation
#math.RT

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Abstract

Let G be a connected reductive group over a p-adic field F, U the unipotent radical of a minimal parabolic subgroup, ψ a depth-zero non-degenerate character of U(F), and I an Iwahori subgroup of G(F). We show that, as a module over the Iwahori-Hecke algebra H, the space of I-fixed vectors in the Gelfand-Graev representation ind_U^Gψ is isomorphic to H ⊗_H_W0 sgn. Here sgn is the sign representation of the finite Hecke subalgebra H_W0 attached to the relative Weyl group. This extends the theorem of Chan-Savin from split groups to all connected reductive groups.

Citations

• Algebraic Groups Over Finite Fields

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