University of Sydney Algebra Seminar

Tomoyuki Arakawa (Research Institute for Mathematical Sciences, Kyoto University)

Friday 19th April, 12:05-12:55pm, Carslaw 373

Affine W-algebras and Vinberg's problem for centralizers

Let \(\mathfrak{g}=\mathfrak{gl}(n,\mathbb{C})\) and \(e\) be a nilpotent element of \(\mathfrak{g}\), \(\mathfrak{g}_e\) the centralizer of \(e\) in \(\mathfrak{g}\). In my talk I will show the existence of a quantization of the Mishchenko-Fomenko algebra in \(S(\mathfrak{g}_e)\) associated with any regular element in the dual of \(\mathfrak{g}_e\). The proof uses affine \(W\)-algebras.