Branching Rules for Principal Series Representations of SL(2) over a p-adic Field

Nevins, Monica

Canadian journal of mathematics, Tome 57 (2005) no. 3, pp. 648-672

Résumé

We explicitly describe the decomposition into irreducibles of the restriction of the principal series representations of $SL\left( 2,\,k \right)$ , for $k$ a $p$ -adic field, to each of its two maximal compact subgroups (up to conjugacy). We identify these irreducible subrepresentations in the Kirillov-type classification of Shalika. We go on to explicitly describe the decomposition of the reducible principal series of $SL\left( 2,\,k \right)$ in terms of the restrictions of its irreducible constituents to a maximal compact subgroup.

Détail

DOI : 10.4153/CJM-2005-026-1

Mots-clés : 20G25, 22E35, 20H25, representations of p-adic groups, p-adic integers, orbit method, K-types

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