Nilpotent Orbits and Representation Theory

Generators of affine W-algebras

speaker: Alexander Molev (University of Sydney)

abstract: We construct explicit generators of the affine W-algebra of type A associated with a nilpotent matrix whose Jordan blocks are of the same size. By applying the quantum Miura transformation we recover the construction of the principal W-algebra of Fateev and Lukyanov. In the classical limit and the critical level we get generators of the respective classical W-algebras. The construction extends to the classical W-algebras associated with the simple Lie algebras of all classical types and the exceptional Lie algebra of type G_2. The generators are given by determinant formulas in the context of the Poisson vertex algebras.

timetable:
Thu 16 Jun, 16:15 - 17:30, Aula Bianchi Scienze
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