Semisimple types for quaternionic forms of p-adic classical groups and compatible beta-extensions

Daniel Skodlerack; Shuyang Ye

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arXiv · 2607.01074

Semisimple types for quaternionic forms of p-adic classical groups and compatible beta-extensions

Daniel Skodlerack·Shuyang Ye

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Abstract

Let $G$ be a quaternionic form of a $p$-adic classical group ($p$ odd). We construct a Bushnell-Kutzko-Stevens type for every Bernstein block of the category of smooth complex representations of $G$. Further we construct a system of compatible $\beta$-extensions, i.e. a family of $\beta$-extensions parametrised by the points of a chamber of the Bruhat-Tits building of the centralizer $G_\beta$ which are related via transfer.

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Daniel Skodlerack, Shuyang Ye. 2026-07-01. Semisimple types for quaternionic forms of p-adic classical groups and compatible beta-extensions. https://arxiv.org/abs/2607.01074

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