Title: Finite W-algebras and their representations
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Abstract: Finite W-algebras are associative algebras
arising in Lie theory. During the last decade they
were extensively studied by Brundan, Ginzburg, Kleshchev,
Premet, the speaker and others. They are related to many
classical representation theoretic objects: semisimple Lie algebras
(both in zero and positive
characteristic), various modifications of Yangians,
Hecke algebras. I will try to give a non-technical
account on the relation between finite W-algebras
and semisimple Lie algebras.