Compact symmetric spaces, triangular factorization, and Cayley coordinates

Details Compact symmetric spaces, triangular factorization, and Cayley coordinates Compact symmetric spaces, triangular factorization, and Cayley coordinates

2008-08-18

arxiv.org/abs/0808.2251v3

Mathematics

Representation Theory

19 pages: Main proof entirely rewritten, sections reorganized, exposition made more precise and concise. To appear in Pacific

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Compact symmetric spaces, triangular factorization, and Cayley coordinates does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Compact symmetric spaces, triangular factorization, and Cayley coordinates, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Compact symmetric spaces, triangular factorization, and Cayley coordinates will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-697105