AbstractLet X_n be the set of tuples of 2x2 matrices (A_1, A_2, ..., A_n) such that the product A_1...A_n is the identity matrix, and considered up to simultaneous conjugation. On each X_n, there is a very classical and explicit action of the so-called braid group B_n. This is an elementary case of the so-called mapping class group action on the character varieties of surface groups, and was st...
Abstract:One of the central foci of representation theory in the 20th century was the representation theory of Lie algebras, starting with finite dimensional algebras and expanding to a rich, but still mysterious infinite dimensional theory. In this century, we realized that this was only one special case of a bigger theory, with new sources of interesting non-commutative algebras whose repres...