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- W4300919511 abstract "Let $F$ be a $p$-adic field. Let $mathcal{R}$ be the Grothendieck ring of complex smooth finite-length representations of the groups ${GL_n(F)}_{n=0}^infty$ taken together, with multiplication defined in the sense of parabolic induction. We introduce a width invariant for elements of $mathcal{R}$ and show that it gives an increasing filtration on the ring. Irreducible representations of width $1$ are precisely those known as ladder representations. We thus obtain a necessary condition on irreducible factors of a product of two ladder representations. For such a product we further establish a multiplicity-one phenomenon, which was previously observed in special cases." @default.
- W4300919511 created "2022-10-04" @default.
- W4300919511 creator A5086993894 @default.
- W4300919511 date "2016-04-25" @default.
- W4300919511 modified "2023-09-25" @default.
- W4300919511 title "A filtration on rings of representations of non-Archimedean $GL_n$" @default.
- W4300919511 doi "https://doi.org/10.48550/arxiv.1604.07333" @default.
- W4300919511 hasPublicationYear "2016" @default.
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