Iwahori component of Bessel model spaces

TL;DR

This paper computes the Iwahori component of Bessel model spaces for special orthogonal groups over p-adic fields, identifying it explicitly with a projective Iwahori-Hecke algebra module.

Contribution

It provides an explicit computation of the Iwahori component of Bessel models and characterizes it as a specific projective module over the Iwahori Hecke algebra.

Findings

Explicit description of the Iwahori component of Bessel models

Identification with a projective Iwahori-Hecke algebra module

Advancement in understanding representations of special orthogonal groups

Abstract

Let $k_0$ be a $p$-adic field of odd residual characteristic, and $G$ a special orthogonal group defined as acting on a split $2n+1$-dimensional orthogonal space $V$ over $k_0$. Let $H$ be the Iwahori Hecke algebra of $G$. A purpose of this short article is to compute the Iwahori component of a Bessel model space and identify it with an explicit projective $H$-module.