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Author Habermas, Derek
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2008-08-18
Language English
Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics
Subject Keyword Mathematics - Representation Theory ♦ 53D17 (Secondary) ♦ 53C35 (Primary) 43A85 ♦ 57T15 ♦ math
Abstract Let U/K represent a connected, compact symmetric space, where theta is an involution of U that fixes K, phi: U/K to U is the geodesic Cartan embedding, and G is the complexification of U. We investigate the intersection of phi(U/K) with the Bruhat decomposition of G corresponding to a theta-stable triangular, or LDU, factorization of the Lie algebra of G. When g in phi(U/K) is generic, the corresponding factorization g=ld(g)u is unique, where l in N^-, d(g) in H, and u in N^+. In this paper we present an explicit formula for d in Cayley coordinates, compute it in several types of symmetric spaces, and use it to identify representatives of the connected components of the generic part of phi(U/K). This formula calculates a moment map for a torus action on the highest dimensional symplectic leaves of the Evens-Lu Poisson structure on U/K.
Educational Use Research
Learning Resource Type Article
Page Count 19


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