Results 41 to 50 of about 670 (58)

Hecke algebras and local Langlands correspondence for non-singular depth-zero representations

Forum of Mathematics, Sigma
Let G be a connected reductive group over a non-archimedean local field. We say that an irreducible depth-zero (complex) G-representation is non-singular if its cuspidal support is non-singular.
Maarten Solleveld, Yujie Xu
doaj   +1 more source

Contragredient representations and characterizing the local Langlands correspondence

, 2015
We consider the question: what is the contragredient in terms of L-homomorphisms? We conjecture that it corresponds to the Chevalley automorphism of the L-group, and prove this in the case of real groups.
Adams, Jeffrey, Vogan Jr, David A.
core   +1 more source

Local parameters of supercuspidal representations

Forum of Mathematics, Pi
For a connected reductive group G over a nonarchimedean local field F of positive characteristic, Genestier-Lafforgue and Fargues-Scholze have attached a semisimple parameter ${\mathcal {L}}^{ss}(\pi )$ to each irreducible representation $\pi $
Wee Teck Gan, Michael Harris, Will Sawin, Raphaël Beuzart-Plessis   +3 more
doaj   +1 more source

Local newforms and formal exterior square L-functions

, 2012
Let F be a non-archimedean local field of characteristic zero. Jacquet and Shalika attached a family of zeta integrals to unitary irreducible generic representations $\pi$ of GL_n(F). In this paper, we show that Jacquet-Shalika integral attains a certain
Miyauchi, Michitaka, Yamauchi, Takuya
core   +1 more source

Doubling constructions and tensor product L-functions: coverings of the symplectic group

Forum of Mathematics, Sigma
In this work, we develop an integral representation for the partial L-function of a pair $\pi \times \tau $ of genuine irreducible cuspidal automorphic representations, $\pi $ of the m-fold covering of Matsumoto of the symplectic group $
Eyal Kaplan
doaj   +1 more source

Geometric structure for the principal series of a split reductive $p$-adic group with connected centre

, 2015
Let $\mathcal{G}$ be a split reductive $p$-adic group with connected centre. We show that each Bernstein block in the principal series of $\mathcal{G}$ admits a definite geometric structure, namely that of an extended quotient.
Aubert, Anne-Marie, Baum, Paul, Plymen, Roger, Solleveld, Maarten   +3 more
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Quasi-polynomial representations of double affine Hecke algebras

Forum of Mathematics, Sigma
We introduce an explicit family of representations of the double affine Hecke algebra $\mathbb {H}$ acting on spaces of quasi-polynomials, defined in terms of truncated Demazure-Lusztig type operators.
Siddhartha Sahi, Jasper Stokman, Vidya Venkateswaran   +2 more
doaj   +1 more source

On the notion of conductor in the local geometric Langlands correspondence

, 2016
Under the local Langlands correspondence, the conductor of an irreducible representation of $\Gl_n(F)$ is greater than the Swan conductor of the corresponding Galois representation.
Kamgarpour, Masoud
core   +1 more source

Eisenstein Cohomology for $\mathrm {GL}_N$ and the special values of Rankin–Selberg L-functions over a totally imaginary number field

Forum of Mathematics, Sigma
This article presents new rationality results for the ratios of critical values of Rankin–Selberg L-functions of $\mathrm {GL}(n) \times \mathrm {GL}(n')$ over a totally imaginary field $F.$ The proof is based on a cohomological ...
A. Raghuram
doaj   +1 more source

Uniqueness of Rankin-Selberg periods [PDF]

, 2013
Let $k$ be a local field of characteristic zero. Rankin-Selberg's local zeta integrals produce linear functionals on generic irreducible admissible smooth representations of $GL_n(k)\times GL_r(k)$, with certain invariance properties.
Chen, Fulin, Sun, Binyong
core