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arXiv · 2604.14823

Formal degree of principal series of quasi-split groups

Giulio Ricci
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Abstract

Let $\mathcal{G}$ be a quasi-split connected reductive group over a non-archimedean local field $F.$ In this paper, we prove the formal degree conjecture for discrete series representations contained in a principal series of $\mathcal{G}(F)$. We first construct a type for each Bernstein component attached to a principal series representation of $\mathcal{G}(F).$ We then use these types and the local Langlands correspondence for principal series representations defined in [Sol25] to verify the formal degree conjecture. Our approach follows a similar strategy to [Ric25], reducing the problem to the case of unipotent representations of some other quasi-split group.

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Giulio Ricci. 2026-04-16. Formal degree of principal series of quasi-split groups. https://arxiv.org/abs/2604.14823

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