Affiliation:
1. Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore, 119076
Abstract
Abstract
Let $\mathcal{R}$ be the Grothendieck ring of complex smooth finite-length representations of the sequence of p-adic groups $\{GL_n(F)\}_{n=0}^\infty $, with multiplication defined through parabolic induction. We study the problem of the decomposition of products of irreducible representations in $\mathcal{R}$. We obtain a necessary condition on irreducible factors of a given product by introducing a width invariant. Width $1$ representations form the previously studied class of ladder representations. We later focus on the case of a product of two ladder representations, for which we establish that all irreducible factors appear with multiplicity one. Finally, we propose a general rule for the composition series of a product of two ladder representations and prove its validity for cases in which the irreducible factors correspond to smooth Schubert varieties.
Funder
Israel Science Foundation
European Research Council
Publisher
Oxford University Press (OUP)
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