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Limit formulas for groups with one conjugacy class of Cartan subgroups

Mladen Božičević (2008)

Annales de l’institut Fourier

Limit formulas for the computation of the canonical measure on a nilpotent coadjoint orbit in terms of the canonical measures on regular semisimple coadjoint orbits arise naturally in the study of invariant eigendistributions on a reductive Lie algebra. In the present paper we consider a particular type of the limit formula for canonical measures which was proposed by Rossmann. The main technical tool in our analysis are the results of Schmid and Vilonen on the equivariant sheaves on the flag variety...

Linear maps preserving orbits

Gerald W. Schwarz (2012)

Annales de l’institut Fourier

Let H GL ( V ) be a connected complex reductive group where V is a finite-dimensional complex vector space. Let v V and let G = { g GL ( V ) g H v = H v } . Following Raïs we say that the orbit H v is characteristic for H if the identity component of G is H . If H is semisimple, we say that H v is semi-characteristic for H if the identity component of G is an extension of H by a torus. We classify the H -orbits which are not (semi)-characteristic in many cases.

Linear periods.

Hervé Jacquet, Solomon Friedberg (1993)

Journal für die reine und angewandte Mathematik

Local geometry of orbits for an ordinary classical lie supergroup

Tomasz Przebinda (2006)

Open Mathematics

In this paper we identify a real reductive dual pair of Roger Howe with an Ordinary Classical Lie supergroup. In these terms we describe the semisimple orbits of the dual pair in the symplectic space, a slice through a semisimple element of the symplectic space, an analog of a Cartan subalgebra, the corresponding Weyl group and the corresponding Weyl integration formula.

Local-global compatibility for l = p , I

Thomas Barnet-Lamb, Toby Gee, David Geraghty, Richard Taylor (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

We prove the compatibility of the local and global Langlands correspondences at places dividing l for the l -adic Galois representations associated to regular algebraic conjugate self-dual cuspidal automorphic representations of GL n over an imaginary CM field, under the assumption that the automorphic representations have Iwahori-fixed vectors at places dividing l and have Shin-regular weight.

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