ΕΚΔΗΛΩΣΕΙΣ

ΓΕΝΙΚΟ ΣΕΜΙΝΑΡΙΟ - WHITTAKER FUNCTIONS FOR STEINBERG REPRESENTATIONS OF GL(N) OVER A P-ADIC FIELD

Thursday 17 Οκτωβρίου 2024

Ημέρα: Πέμπτη 17 Οκτωβρίου
Ώρα: 13:00
Τόπος: Αίθουσα Γ32
Ομιλητής: Μάρκος Καραμέρης από το πανεπιστήμιο του Technion.

Τίτλος: Whittaker functions for Steinberg representations of GL(n) over a p-adic field

Περίληψη: Let G = GLn(F) and let (πSt, V ) be a (generalized) Steinberg representation of G. It is well 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 the value of this character on a particular Hecke algebra element and use this action to determine in full the Whittaker function associated with an Iwahori fixed vector generalizing a result of Baruch and Purkait for GL2(F). This result is essentially a Casselman-Shalika formula analogue for Iwahori spherical vectors. We will demonstrate what this Whittaker function is explicitly and, time permitting, we will discuss how we can use it to compute the Whittaker function attached to a Steinberg representation of SLn(F).

This is joint work with Ehud Moshe Baruch.