arXiv subjects

Daniel Johnstone

Publications and source records attributed to Daniel Johnstone.

2 recordsLinked to original sources

arXiv2020

On the Stable Transfer for $\mathrm{Sym}^{n}$ Lifting of $\mathrm{GL}_{2}$

Following the paradigm of \cite{MR3117742}, we are going to explore the stable transfer factors for $\mathrm{Sym}^{n}$ lifting from $\mathrm{GL}_{2}$ to $\mathrm{GL}_{n+1}$ over any local fields $F$ of characteristic zero with residue characteristic not equal to $2$. When $F=\mathbb{C}$ we construct an explicit stable transfer factor for any $n$. When $n$ is odd, we provide a reduction formula, reducing the question to the construction of the stable transfer factors when the $L$-morphism is the diagonal embedding from $\mathrm{GL}_{2}(\mathbb{C})$ to finitely many copies of $\mathrm{GL}_{2}(\mathbb{C})$ under mild assumptions on the residue characteristic of $F$. With the assumptions on the residue characteristic, the reduction formula works uniformly over any local fields of characteristic zero, except that for $p$-adic situation we need to exclude the twisted Steinberg representations.

math.RT↗

arXiv2016

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

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 local stable transfer factor $\Theta_\phi$ in the sense of \cite{SetT} associated to a natural $L$-embedding $\phi:{^LT}\to{^LG}$ for $G=\text{SL}_\ell$ for $\ell$ an odd prime and $T\subset G$ a maximal unramified elliptic torus defined over $F$. We also explicitly compute the associated stable transfer, answering in the affirmative the Questions A and B of \cite{SetT}. We do the same, explicitly computing the stable transfer factor $\Theta_{\widetilde{\phi}}$ and the associated stable transfer operator, in the related case of $\widetilde{\phi}:{^L\widetilde{T}}\to{^L\widetilde{G}}$ for $\widetilde{G}=\text{GL}_\ell$ and $\widetilde{T}\subset \widetilde{G}$ a maximal unramified elliptic torus defined over $F$.

math.NT↗