A Gelfand-Graev Formula and Stable Transfer Factors in the Unramidied Case for ${\text{SL}}_{\ell }(F)$ and ${\text{GL}}_{\ell }(F)$, $\ell$ an odd Prime

Daniel Johnstone

Let $F$ be a nonarchimedean local field of characteristic 0 with residual characteristic $p$ and let $\ell$ be an odd prime with $2\ell <p$. We establish and explicitly compute the…