most recent 30 from http://mathoverflow.net 2013-05-22T19:41:38Z http://mathoverflow.net/feeds/question/83047 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/83047/does-iwahori-subalgebra-correspond-to-any-cartan-decomposition-for-affine-kac-moo Shizhuo Zhang 2011-12-09T10:33:42Z 2011-12-09T19:09:43Z

<p>Let $\hat{\mathfrak{g}}$ be an affine Kac-Moody algebra which is the central extension of $\mathfrak{g}[t,t^{-1}]$(polynomial version). Consider Iwahori subalgebra $I$. My question is whether $I$ corresponds to some Cartan decomposition for $\hat{\mathfrak{g}}$</p> <p>Further question is if considering "generalized Verma module" corresponding to $I$, i.e. Define $M(\lambda):=U(\hat{\mathfrak{g}})\otimes_{U(I)}\mathbb{C}_\lambda$. Does $M(\lambda)$ in the category $O$ correspoding to this "Iwahori-induction"?</p> <p>Thanks</p>