منابع مشابه
Parabolic subgroups of Garside groups
A Garside monoid is a cancellative monoid with a finite lattice generating set; a Garside group is the group of fractions of a Garside monoid. The family of Garside groups contains the Artin-Tits groups of spherical type. We generalise the well-known notion of a parabolic subgroup of an Artin-Tits group into that of a parabolic subgroup of a Garside group. We also define the more general notion...
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Let G be a reductive algebraic group defined over an algebraically closed field k. Let H be a closed connected subgroup of G containing a maximal torus T of G. In [13] it was shown (at least in characteristic zero) that the parabolic subgroups of G can be characterized among all such subgroups H by a certain finiteness property of the induction functor (-)Iz and its derived functors Lk,G(-). Th...
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Let g be a finite dimensional complex semi-simple Lie algebra with Weyl group W and simple reflections S. For I ⊆ S let gI be the corresponding semi-simple subalgebra of g. Denote by WI the Weyl group of gI and let w◦ and w I ◦ be the longest elements of W and WI , respectively. In this paper we show that the answer to Kostant’s problem, i.e. whether the universal enveloping algebra surjects on...
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Let g be a finite dimensional complex semi-simple Lie algebra with Weyl group W and simple reflections S. For I ⊆ S let g I be the corresponding semi-simple subalgebra of g. Denote by W I the Weyl group of g I and let w • and w I • be the longest elements of W and W I , respectively. In this paper we show that the answer to Kostant's problem, i.e. whether the universal enveloping algebra surjec...
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Definition 1. Let G be a permutation group on a set and x be an element of . Then Gx g ∈ G ∣ gx x is called the stabilizer of x and consists of all the permutations of G that produce group fixed points in x. Definition 2. A vector subspace S ⊂ V is isotropic if for any v,w ∈ S, the symmetric bilinear form satisfies: Bv,w 0 Definition 3. A maximal parabolic subgroup in an orthogon...
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2013
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2013.13.3203