Year: 2024
Type: preprint
Abstract: Let $G(F)$ be a split reductive group over a $p$-adic field $F$ and let $(π_{St},V)$ be a (generalized) Steinberg representation of $G(F)$. It is known that the space of Iwahori fixed vectors in $V$ is one dimensional. The Iwahori Hecke algebra acts on this space via a character. We determine this fixed vector and use the Hecke algebra action on it to determine in full the Whittaker function associated with this Iwahori fixed vector. This generalizes our previous result for $GL_n(F)$.
Source: arXiv (Cornell University)
Authors: Karameris, Markos, Baruch, Ehud Moshe
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4400340513