Speh representations are relatively discrete

Autor: Jerrod Manford Smith

Publikováno v: Representation Theory of the American Mathematical Society. 24:525-550

Let $F$ be a $p$-adic field of characteristic zero and odd residual characteristic. Let $\mathbf{Sp}_{2n}(F)$ denote the symplectic group defined over $F$, where $n\geq 2$. We prove that the Speh representations $\mathcal{U}(\delta,2)$, where $\delta

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ebf5d0fa2f7896e55488255db02d5406
https://doi.org/10.1090/ert/550

Discrete series multiplicities for classical groups over $\mathbf {Z}$ and level 1 algebraic cusp forms

Autor: Olivier Taïbi, Gaëtan Chenevier

Publikováno v: Publications mathématiques de l'IHÉS. 131:261-323

The aim of this paper is twofold. First, we introduce a new method for evaluating the multiplicity of a given discrete series representation in the space of level 1 automorphic forms of a split classical group $G$ over $\mathbf {Z}$ , and provide num

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::ab0958cc5cb1530f8d1cf3d9f66a4328
https://doi.org/10.1007/s10240-020-00115-z

The density theorem for discrete series representations restricted to lattices

Autor: Jordy Timo van Velthoven, José Luis Romero

Publikováno v: Expositiones Mathematicae, 40(2)

This article considers the relation between the spanning properties of lattice orbits of discrete series representations and the associated lattice co-volume. The focus is on the density theorem, which provides a trichotomy characterizing the existen

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c1e5ecb184dceed64024198fcc65a276
http://resolver.tudelft.nl/uuid:57b5a7a3-1487-4439-8c7f-3ab15bb4347c

Ellipticity and discrete series

Autor: Job J. Kuit, Bernhard Krötz, Eric Opdam, Henrik Schlichtkrull

Publikováno v: Journal fur die Reine und Angewandte Mathematik, 2022(782), 109-119. De Gruyter
Krötz, B, Kuit, J J, Opdam, E M & Schlichtkrull, H 2022, ' Ellipticity and discrete series ', Journal fur die Reine und Angewandte Mathematik, vol. 2022, no. 782, pp. 109-119 . https://doi.org/10.1515/crelle-2021-0063

We explain by elementary means why the existence of a discrete series representation of a real reductive group G implies the existence of a compact Cartan subgroup of G. The presented approach has the potential to generalize to real spherical spaces.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::89b57e7942224dd2dce95470d644a568
https://dare.uva.nl/personal/pure/en/publications/ellipticity-and-discrete-series(117ae31a-16b9-45b5-a829-daee9d06fc8c).html

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