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Type I Howe Duality over Finite Fields https://arxiv.org/abs/2412.15346 #mathRT

Type I Howe Duality over Finite Fields

In this paper, we consider higher tensor powers of oscillator representations over finite fields. We find a decomposition of their endomorphism algebras into group algebras of orthogonal groups, giving a new version of Howe duality for a certain range of Type I reductive dual pairs. Specifically, we find that all occurring terms arise from parabolic inductions and the eta correspondence of R. Howe and S. Gurevich. This also leads to a version of Howe duality in a certain category "interpolating" the oscillator representations.

arXiv.org
December 24, 2024 at 3:10 AM · · feed2toot · 0 · 0 · 0
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