Abstract: Let E/F be a quadratic extension of finite fields, \(G=GL(n,E)\), and let \(H\) be one of the groups \(GL(n,F)\) or \(U(n,E/F)\), and \(H'\) be the other one. It is known by the work of Gow that irreducible \(H\)-distinguished representations of \(G\) are those obtained from base changing a representation of \(H'\). If \(\pi=BC_{H'}^G(\rho)\) is a generic \(H\)-distinguished representation of \(G\), we will give a formula for the \(H\)-period of its Bessel function, expressed in terms of \(\dim(\rho)\), and discuss some consequences of this formula. If time allows we will also discuss a \(p\)-adic analogue of the formula. This is a joint work with U.K. Andandavardhanan.
Base change and periods of Bessel functions for \(GL(n,q^2)\)
02.04.2019 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: