Mathematics Colloquia and Seminars

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In this talk we will explain the role of Brauer algebras in classical and super Lie theory. We will then focus on the cases where it is not necessarily semisimple and study their (generalized) branching graphs. This gives rise to generalizations of standard tableaux which keep track of the non-semisimplicity as well. In case of the symmetric group, the branching is connected with the action of a Lie algebra (respectively quantum group). We explain the analogue situation for Brauer algebras. In this way we naturally arise at quantum symmetric pairs which are certain coideals in quantum groups. If time allows we will indicate connections to KLR algebras.