Abstract:In this article, we will prove that the formal degree conjecture is compatible with the Deligne-Kazhdan correspondence for quasi-split groups, assuming that the local Langlands correspondence is compatible with the Deligne-Kazhdan correspondence. Consequently, we establish the formal degree conjecture for $\operatorname{GL}_n$ over local function fields of characteristic $p > 0$, and for $\operatorname{Sp}_{2n}$, split $\operatorname{SO}_{2n}$, $\operatorname{SO}_{2n+1}$, and $\operatorname{GSp}_4$ over local function fields of characteristic $p > 2$.
| Subjects: | Representation Theory (math.RT) |
| MSC classes: | 22E50, 11F70 |
| Cite as: | arXiv:2605.26031 [math.RT] |
| (or arXiv:2605.26031v1 [math.RT] for this version) | |
| https://doi.org/10.48550/arXiv.2605.26031 arXiv-issued DOI via DataCite (pending registration) |
From: Anantha Krishna B [view email]
[v1]
Mon, 25 May 2026 16:59:57 UTC (30 KB)
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