Questions tagged [supercuspidal-representations]
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On a theorem of Bernstein-Zelevinsky regarding supercuspidal resentations
Let $G$ be a $p$-adic reductive group and $\pi$ an irreducible non-supercuspidal representation. Then there exist a parbaolic subgroup $P=MN$ and a supercuspidal representation of $M$ such that $\pi$ ...
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Level vs. conductor of a supercuspidal representation
What is the relation between level and conductor of a supercuspidal representation of $\operatorname{GL}_2(\mathbb{Q}_p)$ for some prime $p$?
Proposition 3.4 in Loeffler and Weinstein - On the ...
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A question related to supercuspidal representations of $\operatorname{GL}_2$ over local fields
I was learning about the representation of $\operatorname{GL}_2$ over local fields and came to know something like: if the residual characteristic of the local field is an odd prime, then every ...
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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 ...
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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 $\...
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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_{...
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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 ...
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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 ...
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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 $s \in \mathbb{C}$ ...
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