Sphericity and multiplication of double cosets for infinite-dimensional classical groups
نویسندگان
چکیده
منابع مشابه
Parabolic Double Cosets in Coxeter Groups
Parabolic subgroups WI of Coxeter systems (W,S), as well as their ordinary and double quotients W/WI and WI\W/WJ , appear in many contexts in combinatorics and Lie theory, including the geometry and topology of generalized flag varieties and the symmetry groups of regular polytopes. The set of ordinary cosets wWI , for I ⊆ S, forms the Coxeter complex of W , and is well-studied. In this article...
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We study a class of double coset spaces RA\G1 × G2/RC , where G1 and G2 are connected reductive algebraic groups, and RA and RC are certain spherical subgroups of G1×G2 obtained by “identifying” Levi factors of parabolic subgroups in G1 and G2. Such double cosets naturally appear in the symplectic leaf decompositions of Poisson homogeneous spaces of complex reductive groups with the Belavin–Dri...
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Regular Lie groups are infinite dimensional Lie groups with the property that smooth curves in the Lie algebra integrate to smooth curves in the group in a smooth way (an ‘evolution operator’ exists). Up to now all known smooth Lie groups are regular. We show in this paper that regular Lie groups allow to push surprisingly far the geometry of principal bundles: parallel transport exists and fla...
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ژورنال
عنوان ژورنال: Functional Analysis and Its Applications
سال: 2011
ISSN: 0016-2663,1573-8485
DOI: 10.1007/s10688-011-0025-6