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pro vyhledávání: '"Afgoustidis, Alexandre"'
Autor:
Adams, Jeffrey, Afgoustidis, Alexandre
Let $G(\mathbb{R})$ be a real reductive group. Suppose $\pi$ is an irreducible representation of $G(\mathbb{R})$ having a Whittaker model, and consider three invariants of $\pi$ related to nilpotents elements of the Lie algebra of $G$ (or its dual):
Externí odkaz:
http://arxiv.org/abs/2410.04134
Autor:
Afgoustidis, Alexandre
Ce texte, \'ecrit pour la Gazette de la Soci\'et\'e math\'ematique de France, \'evoque les fonctions de type positif et leur histoire avant 1950 ; on y pr\'esente notamment des extraits de lettres \'ecrites par Roger Godement, qui leur consacra sa th
Externí odkaz:
http://arxiv.org/abs/2409.08668
Autor:
Adams, Jeffrey, Afgoustidis, Alexandre
Consider the irreducible representations of a real reductive group $G(\mathbb{R})$, and their parametrization by the local Langlands correspondence. We ask: does the parametrization give easily accessible information on the restriction of representat
Externí odkaz:
http://arxiv.org/abs/2402.03552
Autor:
Afgoustidis, Alexandre
Let $G$ be a reductive group over a nonarchimedean local field $F$. In the quest for a classification of irreducible smooth representations of $G$, it is critical to understand the case of supercuspidal representations -- those whose matrix coefficie
Externí odkaz:
http://arxiv.org/abs/2311.11736
Let $G$ be a real or $p$-adic reductive group. We consider the tempered dual of $G$, and its connected components. For real groups, Wassermann proved in 1987, by noncommutative-geometric methods, that each connected component has a simple geometric s
Externí odkaz:
http://arxiv.org/abs/2002.12864
Publikováno v:
Pacific J. Math. 310 (2021) 257-273
When $G$ is a real reductive group and $G_0$ is its Cartan motion group, the Mackey-Higson bijection is a natural one-to-one correspondence between all irreducible tempered representations of $G$ and all irreducible unitary representations of $G_0$.
Externí odkaz:
http://arxiv.org/abs/1901.00144
Autor:
Afgoustidis, Alexandre
Publikováno v:
Duke Math. J. 169, no. 5 (2020), 897-960
Attached to any reductive Lie group $G$ is a "Cartan motion group" $G_0$ $-$ a Lie group with the same dimension as $G$, but a simpler group structure. A natural one-to-one correspondence between the irreducible tempered representations of $G$ and th
Externí odkaz:
http://arxiv.org/abs/1808.09525
Autor:
Afgoustidis, Alexandre
Publikováno v:
Journal of Functional Analysis 277 (2019), no. 7, 2237-2258
Alain Connes and Nigel Higson pointed out in the 1990s that the Connes-Kasparov "conjecture"' for the K-theory of reduced groupe $C^\ast$-algebras seemed, in the case of reductive Lie groups, to be a cohomological echo of a conjecture of George Macke
Externí odkaz:
http://arxiv.org/abs/1602.08891
Autor:
Afgoustidis, Alexandre
Publikováno v:
Proceedings of the AMS 146 (2018), no. 9, 3747-3758
We prove that if $X$ is a symmetric space of the noncompact type, just as adding Helgason waves which propagate in all direction yields an elementary spherical function for $X$, a Helgason wave can be produced by adding elementary spherical functions
Externí odkaz:
http://arxiv.org/abs/1602.03871
Autor:
Afgoustidis, Alexandre
We review and study some of the properties of smooth Gaussian random fields defined on a homogeneous space, under the assumption that the probability distribution is invariant under the isometry group of the space. We first give an exposition, buildi
Externí odkaz:
http://arxiv.org/abs/1602.02560