Spherical conjugacy classes and the Bruhat decomposition
نویسندگان
چکیده
منابع مشابه
On Intersections of Conjugacy Classes and Bruhat Cells
For a connected complex semi-simple Lie group G and a fixed pair (B, B−) of opposite Borel subgroups of G, we determine when the intersection of a conjugacy class C in G and a double coset BwB− is non-empty, where w is in the Weyl group W of G. The question comes from Poisson geometry, and our answer is in terms of the Bruhat order on W and an involution mC ∈ W associated to C. We study propert...
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Let (G,B,N, S) be a Tits system. Some aspects of intersections of conjugacy classes ofG with Bruhat cellsBẇB have been investigated by several authors (see e.g., [St1], [K], [V] and [VS]). Here w ∈ W = N/(B ∩N) and ẇ ∈ N is a preimage of w with respect to the natural surjection N → W . In particular, it is desirable to learn how a conjugacy class C of G is related to those conjugacy classes Cw ...
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For each parallel class Pi , 1 ≤ i ≤ n there corresponds a permutation σi acting on the letter set {1, 2, . . . , n} as follows: σi (k) = l iff (k, l) is an arc of Pi . Let G be the group generated by σ1, σ2, . . . , σn . The given configuration is inner transitive if G permutes the parallel classes transitively. In this paper we study the interaction between an inner-transitive Hering configur...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2009
ISSN: 0373-0956,1777-5310
DOI: 10.5802/aif.2492