All Questions

Let $G$ be a compact, simple, connected, simply connected (cscsc) Lie group, and let its smooth loop group $LG:=C^\infty(S^1,G)$. Given an interval $I\subset S^1$, we have the local loop group $$ L_IG ...

At the end of Section 14.1 in Pressley, Segal "Loop Groups" there is the remark that the partition function is a modular function in the sense that the Dedekind $\eta$ function is a modular form. I ...

The Geometric Satake correspondence (due to Lusztig, Ginzburg, Mirkovic-Vilonen) relates perverse sheaves on the Loop Group $\hat{G}$ (with their convolution product) to the Representations of the ...

Let $X$ be a scheme over $K = k((t))$, where $k$ is a field. We define the loop scheme $LX$ to be the functor from the category of $k$-algebras to sets by $R \mapsto LX(R) := X(Spec (R((t))))$. Do we ...

I'm interested in an infinite dim'l Heisenberg group associated to the vector space $V = L\mathbb{C}/\mathbb{C}$ = {$f \colon S^1 \to \mathbb{C}$|$f$ smooth}/(const. maps). The group is $\mathbb{C}^\...