Comparison of the Sally-Shalika character formulas with the endoscopic character identities for $\mathrm{SL}_2$
Year: 2024
Type: preprint
Abstract: We consider the depth-zero supercuspidal $L$-packets of $\mathrm{SL}_2(F)$ where $F$ is a non-archimedean local field of characteristic zero. We compare the explicit endoscopic character identities for $\mathrm{SL}_2(F)$ with the classical character formulas of Sally-Shalika. Our main result concerns the supercuspidal $L$-packet of size $4$. For this $L$-packet, we show how the norm $1$ groups $H_1, H_2, H_3$ in the three quadratic extensions of $F$ play a crucial role in the endoscopic character identities for $\mathrm{SL}_2(F)$.
Source: arXiv (Cornell University)
Authors: Aubert, Anne-Marie, Plymen, Roger
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4404313817