Endoscopic character identities for depth-zero supercuspidal representations of $\mathrm{SL}_2$
Résumé
We consider the depth-zero supercuspidal $L$-packets of $\mathrm{SL}_2$. With the aid of the classical character formulas of Sally-Shalika, we prove the endoscopic character identities. We comment on the truth-status of Theorem 15.2 in the 2011 article by Adler, DeBacker, Sally and Spice.
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