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Let $F$ be a local field and $G = GL(n,F)$. Let $f$ be an element $C_c^\infty(G)$. Let $\gamma$ be an elliptic element of $G$ with irreducible characteristic polynomial. What are strategies to compu …

Let $\pi$ be a supercuspidal representation of $G =GL_2(F)$ for a non-archimedean local field $F$, then there exists a maximal subgroup $K$ of $G$, which is compact modulo the center, and a representa …

Let $G$ be an locally compact group $G$, then every irreucible representations $\pi$ is isomorphic to $\omega_{\pi} \otimes \pi'$, where $\omega_{\pi}$ is the central character of $\pi$ and $\pi'$ an …

I have one issue with the Jacquet Langlands correspondence. The Weyl law for $H$ modulo a congruence subgroup and the Weyl law for cocompact groups are different. So why does this not contradict this …

Let $F_v$ be a local field. Let $\sigma_v$ be a two-dimensional representation of $Gal(\overline{F}_v:F_v) \rtimes W_{F_v}$. Now, there exists an infinite-dimensional representation $\pi_v$ of $GL_2(F …

Let $F$ be a local field and $G= GL(n,F)$. Assume that $\gamma$ is an element of $G$ and $G_\gamma$ is its centralizer. The orbital integral is defined as $$ O_\gamma^G( \phi) = \int\limits_{G_\gamm …

The cuspidal representations of $\operatorname{GL}_n(F)$ a non archimedean field $F$ with ring of integers $o$ can be classified by inducing irreducible representation from $Z\operatorname{GL}_n(o)$. …

Edit due to the comment. Consider $G=GL(2)$ over a local field $F$. The Fell topology on the unitary dual of $G(F)$ is seperable. Given a sequence of irreducible unitary representations $(\pi_n)$ of …

What are some concrete examples of theorems which can be deduced from the Arthur trace formula, which do not follow from the simple trace of Kazdhan and Flicker? (So I do not mean weaker in the sense …

Considering the Arthur trace formula, why are the sort of convolution operators, whose "normalized traces" are given in geometric terms and spectral terms, actually able to distinguish all automorphic …

Let $G$ be a locally profinite group and $K$ an open compact subgroup (mod the center), then Bushnell has shown that the following three statements are equivalent for a finite dimensional representati …

I have read that there is an elementary way to show that the above mentioned trace fromulas are equivalent in the sense, that each of them can be derived directly from the other. There should exist a …

Shimura lifts are correspondence between integer weight and half-integral weight automorphic forms. Half integral weight things are associated to representation of a double cover of $G =SL_2(\mathbb{R …