Branching Rules for Supercuspidal Representations of SL_2(k)

Abstract

The restriction of a supercuspidal representation of SL_2(k), for k a local nonarchimedean field, to a maximal compact subgroup decomposes as a multiplicity-free direct sum of irreducible representations. We explicitly describe this decomposition in the case that the residual characteristic is odd, and determine how the spectrum of this decomposition varies as a function of the parameters describing the supercuspidal representation.

30 pages; minor reorganization to previous version. Accepted to Journal of Algebra

References in corpus (3)

• Restriction de la représentation de Weil à un sous-groupe compact maximal ou à un tore maximal elliptique
• Branching rules for ramified principal series representations of GL(3) over a p-adic field
• Branching rules for unramified principal series representations of GL(3) over a p-adic field