Branching rules for irreducible supercuspidal representations of unramified U(1,1)

2025/11/12 by Tiwari, Ekta
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2511.09033

Abstract

Let G denote the unramified quasi-split unitary group \mathbbU(1,1)(F) over a p-adic field F with residual characteristic p ≠ 2. In this article, we determine the branching rules for all irreducible supercuspidal representations of G, that is, we explicitly describe their decomposition upon restriction to a fixed maximal compact subgroup K in terms of irreducible representations of K. We also present two applications of these decompositions, which verify two new conjectures in the literature for G. Together with the results from a previous paper by the author, this article completes the description of the branching rules for all irreducible smooth representations of G.

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