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arXiv · 1910.13109

On the Howe correspondence and Harish-Chandra series

Jesua Epequin
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Abstract

We study the effect of the Howe correspondence on Harish-Chandra series for type I dual pairs ($\mathbf{U}_m(\mathbb{F}_q),\mathbf{U}_n(\mathbb{F}_q$)) and ($\mathbf{Sp}_{2m}(\mathbb{F}_q),\mathbf{O}^\pm_{2n}(\mathbb{F}_q)$), where $\mathbb{F}_q$ denotes the finite field with $q$ elements ($q$ odd). We use the Lusztig correspondence to reduce the study of the Howe correspondence between Harish-Chandra series to a correspondence between unipotent Harish-Chandra series. Finally, we provide two applications of these results.

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Jesua Epequin. 2019-10-29. On the Howe correspondence and Harish-Chandra series. https://arxiv.org/abs/1910.13109

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