The Bernstein-Gelfand-Gelfand complex and Kasparov theory for SL(3,C)

Details The Bernstein-Gelfand-Gelfand complex and Kasparov theory for SL(3,C) The Bernstein-Gelfand-Gelfand complex and Kasparov theory for SL(3,C)

2008-02-14

arxiv.org/abs/0802.2094v3

Mathematics

Operator Algebras

Complete rewrite. Paper has been rewritten to take advantage of the paper "Products of Longitudinal Pseudodifferential Operato

Scientific paper

Let $G=\mathrm{SL}(3,\mathbb{C})$. We construct an element of $G$-equivariant $K$-homology from the Bernstein-Gelfand-Gelfand complex for $G$. This furnishes an explicit splitting of the restriction map from the Kasparov representation ring $R(G)$ to the representation ring $R(K)$ of its maximal compact subgroup, and the splitting factors through the equivariant $K$-homology of the flag variety of $G$. In particular, we obtain a new model for the gamma element of $G$. The proof makes extensive use of earlier results of the author concerning harmonic analysis of longitudinal psuedodifferential operators on the flag variety.

Affiliated with

Also associated with

No associations

Rating

The Bernstein-Gelfand-Gelfand complex and Kasparov theory for SL(3,C) 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 The Bernstein-Gelfand-Gelfand complex and Kasparov theory for SL(3,C), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Bernstein-Gelfand-Gelfand complex and Kasparov theory for SL(3,C) will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-37317