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pro vyhledávání: '"Opdam, Eric"'
This is a slightly edited translation of a paper in Dutch which appeared in Nieuw Archief voor Wiskunde (5) 25 (2024), No.2, 87-90 on the occasion of I.G. Macdonald's death in 2023, and aimed at a very broad mathematical audience. First we review som
Externí odkaz:
http://arxiv.org/abs/2410.07882
Autor:
De Martino, Marcelo, Opdam, Eric
For an algebraic torus defined over a local (or global) field $F$, a celebrated result of R.P. Langlands establishes a natural homomorphism from the group of continuous cohomology classes of the Weil group, valued in the dual torus, onto the space of
Externí odkaz:
http://arxiv.org/abs/2410.06346
Autor:
Opdam, Eric, Solleveld, Maarten
We further develop the abstract representation theory of affine Hecke algebras with arbitrary positive parameters. We establish analogues of several results that are known for reductive p-adic groups. These include: the relation between parabolic ind
Externí odkaz:
http://arxiv.org/abs/2309.04829
Let $G$ be a split reductive group over a number field $F$. We consider the computation of the inner product of two $K$-spherical pseudo Eisenstein series of $G$ supported in $[T,\mathcal{O}(1)]$ by means of residues, following a classical approach i
Externí odkaz:
http://arxiv.org/abs/2207.06773
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 spa
Externí odkaz:
http://arxiv.org/abs/2007.15312
Publikováno v:
J. Inst. Math. Jussieu (2021)
Let G be a reductive p-adic group which splits over an unramified extension of the ground field. Hiraga, Ichino and Ikeda conjectured that the formal degree of a square-integrable G-representation $\pi$ can be expressed in terms of the adjoint $\gamm
Externí odkaz:
http://arxiv.org/abs/1910.07198
Autor:
Opdam, Eric
Hiraga, Ichino and Ikeda have conjectured an explicit expression for the Plancherel density of the group of points of a reductive group defined over a local field $F$, in terms of local Langlands parameters. In these lectures we shall present a proof
Externí odkaz:
http://arxiv.org/abs/1807.10232
Publikováno v:
Journal de l'\'Ecole polytechnique Math\'ematiques 7 (2020), 1133-1193
Let K be a non-archimedean local field and let G be a connected reductive K-group which splits over an unramified extension of K. We investigate supercuspidal unipotent representations of the group G(K). We establish a bijection between the set of ir
Externí odkaz:
http://arxiv.org/abs/1805.01888
Publikováno v:
Geom. Funct. Anal. 30 (2020), 804 - 857
Let $Z=G/H$ be the homogeneous space of a real reductive group and a unimodular real spherical subgroup, and consider the regular representation of $G$ on $L^2(Z)$. It is shown that all representations of the discrete series, that is, the irreducible
Externí odkaz:
http://arxiv.org/abs/1711.08635
Autor:
Ciubotaru, Dan, Opdam, Eric
In this paper, we consider the relation between two nonabelian Fourier transforms. The first one is defined in terms of the Langlands-Kazhdan-Lusztig parameters for unipotent elliptic representations of a split p-adic group and the second is defined
Externí odkaz:
http://arxiv.org/abs/1604.00604