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The Orbit Method for Complex Groups

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If you have a question about this talk, please contact Gareth Tracey.

The classification of all irreducible unitary representations of a reductive Lie group G is one of the fundamental unsolved problems in representation theory. In the 1960s, Kostant and Kirillov proved that the irreducible unitary representations of a solvable Lie group are (approximately) classified by co-adjoint orbits of G. In the 1980s, David Vogan conjectured that a version of this result should hold for semisimple Lie groups. This set of theorems (in the solvable case) and conjectures (in the reductive case) is referred to as the “Orbit Method”. In recent joint work with Ivan Losev and Dmitryo Matvieievskyi, we define an orbit method correspondence for complex reductive algebraic groups (regarded as real groups by restriction of scalars). I will report on this work and discuss possible extensions to the case of real groups.

This talk is part of the Algebra seminar series.

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