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 (6)

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• A note on Bruhat decomposition of GL(n) over local principal ideal rings
• Restriction de la représentation de Weil à un sous-groupe compact maximal ou à un tore maximal elliptique
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Cited by in corpus (3)

• Typical representations via fixed point sets in Bruhat--Tits buildings
• The local character expansion as branching rules: nilpotent cones and the case of $\mathrm{SL}(2)$
• Representations of $S{L}_2(F)$