Branching rules for ramified principal series representations of GL(3) over a p-adic field

Details Branching rules for ramified principal series representations of GL(3) over a p-adic field Branching rules for ramified principal series representations of GL(3) over a p-adic field

2007-10-17

arxiv.org/abs/0710.3263v1

Mathematics

Representation Theory

18 pages

Scientific paper

We decompose the restriction of ramified principal series representations of the $p$-adic group $\mathrm{GL}(3,\mathrm{k})$ to its maximal compact subgroup $K=\mathrm{GL}(3,\mathscr{R})$. Its decomposition is dependent on the degree of ramification of the inducing characters and can be characterized in terms of filtrations of the Iwahori subgroup in $K$. We establish several irreducibility results and illustrate the decomposition with some examples.

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