AbstractWe will explain a bijection between admissible representations of affine Kac-Moody algebras and fixed points in affine Springer fibers. Furthermore, we can also match the modular group action on the characters with the one defined by Cherednik in terms of double affine Hecke algebras. We will also explain how to extend these relations to representations of W-algebras. This is based on j...
AbstractLet A be an arbitrary associative algebra. With the help of Olshanski’s centralizer construction one can define a sequence Y_1(A), Y_2(A),... of "Yangian-type algebras" (they possess a number of properties of the Yangians of series A). I will discuss a link between these Yangian-type algebras and a class of double Poisson brackets on free associative algebras. The talk is based on the ...
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