Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

I recently learned of a relationship between the representations of the groups $SO(p,q)$ and $SL(2,\mathbb{R})$ which is part of an apparently much larger set of ideas known as Howe Duality. My question is a bit open ended, but can someone point me to a good entry point (review articles, lectures) for learning more about Howe duality and in particular the $SO(p,q)$-$SL(2,\mathbb{R})$ duality? Thanks.

share|improve this question
    
It is related to Capelli identities see wiki and ref therein. Sorry need to run now. –  Alexander Chervov Jan 23 '12 at 7:08
    
See also mathoverflow.net/questions/85562/… –  Alexander Chervov Jan 24 '12 at 5:58

2 Answers 2

up vote 5 down vote accepted

A good introduction is "Non-Abelian Harmonic Analysis: Applications of SL(2,R)" by Roger Howe and Eng Chye Tan, especially Chapter III, Section 2.

share|improve this answer
    
Jeffrey -- thanks for the reference -- and for your previous answer to what is known about the unitary dual of $O(p,q)$. –  Mark Mueller Jan 23 '12 at 22:03
    
To complete the reference Jeff makes, this readable softcover book is published in the Universitext series by Springer-Verlag, New York, 1992. –  Jim Humphreys Jan 29 '12 at 18:34

Have you looked in this?

MR0986027 (90h:22015a) Howe, Roger . Remarks on classical invariant theory. Trans. Amer. Math. Soc. 313 (1989), no. 2, 539--570.

share|improve this answer
    
Thanks -- looks helpful. –  Mark Mueller Jan 23 '12 at 22:04

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.