Some regular symmetric pairs

Details Some regular symmetric pairs Some regular symmetric pairs

2008-05-16

arxiv.org/abs/0805.2504v2

Trans. Amer. Math. Soc. 362 (2010), 3757-3777

Mathematics

Representation Theory

18 pages, 2 figures. v2: minor correction in sections 4.2 and 5.1. To appear in Transactions of the AMS

Scientific paper

In [AG2] we explored the question what symmetric pairs are Gelfand pairs. We introduced the notion of regular symmetric pair and conjectured that all symmetric pairs are regular. This conjecture would imply that many symmetric pairs are Gelfand pairs, and in particular that any connected symmetric pair over C is a Gelfand pair. In this paper we show that the pairs $$(GL(V),O(V)), (GL(V),U(V)), (U(V),O(V)), (O(V \oplus W),O(V) \times O(W)), (U(V \oplus W),U(V) \times U(W))$$ are regular where V and W are quadratic or hermitian spaces over arbitrary local field of characteristic zero. We deduce from that that the pairs $(GL_n(\C),O_n(\C))$ and $(O_{n+m}(\C),O_n(\C) \times O_m(\C))$ are Gelfand pairs.

Affiliated with

Also associated with

No associations

Rating

Some regular symmetric pairs 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 Some regular symmetric pairs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Some regular symmetric pairs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-272824