Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [supercuspidal-representations]

4
votes
0answers
44 views

Conceptual meaning of generalized Kloosterman sums for cuspidal representations

Piatetski-Shapiro, in §13 of his book on complex representations of $GL_2(\mathbf F_q)$, constructs cuspidal representations out of non-decomposable characters $\nu: L^\times \to \mathbf C^\times$ of ...
5
votes
0answers
111 views

Arithmetic of Cuspidal Reps. Fundamental non split stratum and simple stratum

I started to read Colin Bushnell's notes on this title. The last theorem in the 3rd section claims that if $\pi$ is an irr. smooth rep. of $GL_N(F)$ containing a non-split fundamental stratum, then $\...
4
votes
1answer
342 views

Local Galois representation associated to twist of modular form

Let $f$ be a modular newform of weight $k \geq 2$, level $N$ (square free) and trivial nebentypus. Let $V_{f}$ be the $p$-adic (p odd) Galois representation associated $f$. We denote by $V_{f,l}:= V_{...
10
votes
0answers
227 views

Haar measure on $PGL(2,\mathbb{Q}_p)$, the local Jacquet-Langlands correspondence, and Ihara's theorem

Goal. I would like to calculate the product of the formal dimension of a discrete series representation of $GL(2,\mathbb{Q}_p)$ with trivial central character (so, an irreducible unitary ...
1
vote
0answers
138 views

Invariant vectors in supercuspidal representations of GL_2(Zp)

Let $o$ be the ring of integers in a local field $F$ with prime-ideal $p$. Let $K$ be either $GL_2(o)$ or the normalizer of the Iwahori subgroup. Let $\sigma$ be a representation of $K$ times the ...
4
votes
1answer
157 views

Are supercuspidal reps of GL(2) uniquely determined by the rootnumber

Let $\pi, \pi'$ be a unitary, irreducible, supercuspidal representations of $GL_2(F)$. Does an equality of roots numbers $\epsilon(\pi, \psi, s) = \epsilon(\pi', \psi, s)$ for all $s \in \mathbb{C}$ ...