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Spherical conjugacy classes and the Bruhat decomposition

Giovanna Carnovale (2009)

Annales de l’institut Fourier

Let G be a connected, reductive algebraic group over an algebraically closed field of zero or good and odd characteristic. We characterize spherical conjugacy classes in G as those intersecting only Bruhat cells in G corresponding to involutions in the Weyl group of  G .

Spherical roots of spherical varieties

Friedrich Knop (2014)

Annales de l’institut Fourier

Brion proved that the valuation cone of a complex spherical variety is a fundamental domain for a finite reflection group, called the little Weyl group. The principal goal of this paper is to generalize this theorem to fields of characteristic unequal to 2. We also prove a weaker version which holds in characteristic 2, as well. Our main tool is a generalization of Akhiezer’s classification of spherical varieties of rank 1.

Spherical varieties and Wahl’s conjecture

Nicolas Perrin (2014)

Annales de l’institut Fourier

Using the theory of spherical varieties, we give a type independent very short proof of Wahl’s conjecture for cominuscule homogeneous varieties for all primes different from 2.

Springer fiber components in the two columns case for types A and D are normal

Nicolas Perrin, Evgeny Smirnov (2012)

Bulletin de la Société Mathématique de France

We study the singularities of the irreducible components of the Springer fiber over a nilpotent element N with N 2 = 0 in a Lie algebra of type A or D (the so-called two columns case). We use Frobenius splitting techniques to prove that these irreducible components are normal, Cohen–Macaulay, and have rational singularities.

Currently displaying 381 – 400 of 807