Inducing factor representations

I have an infinite dimensional Lie group $G$ of the form $\varinjlim G_n$, for example $SU(9,\infty)$ or $Sp(\infty,R)$. I also have a closed subgroup $P$ of $G$ and a factor representation $\chi$ of $P$ (say on the Hilbert space $H_\chi$). I can use the universal enveloping algebra $U(\mathfrak g)$ to form the induced representation $\pi = Ind_P^G(\chi)$ of $G$ on $U(\mathfrak g) \otimes_P\, H_\chi$.

Has anyone studied the properties of $\pi$? For example: if $\chi$ is factorial of type $II_1$, can $\pi$ be described in terms of factor representations? Any pointers or references would be appreciated.

edited Oct 13 2011 at 19:57

asked Oct 13 2011 at 18:56

Joseph Wolf
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How did you get the letters so big? – Will Jagy Oct 13 2011 at 19:20

By putting ======= under the text. I doubt it was his intention. – darij grinberg Oct 13 2011 at 19:31

I liked it, my near vision keeps getting worse and worse, it may be time for full-time glasses, not just reading glasses for books and the computer screen. I can see how it would not do for a long post. – Will Jagy Oct 13 2011 at 20:14

Welcome to MathOverflow! – Noah Snyder Oct 14 2011 at 4:07

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