q-W algebras, Mickelsson algebras and Zhelobenko operators

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• Alexey Sevastyanov (University of Aberdeen)
• Thursday 20 June 2024, 16:00-16:30
• External.

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TRHW02 - International Conference

q-W algebras were introduced in the mid 90th as q-analogues of W-algebras and as hypothetical symmetry algebras  for massive two-dimensional quantum field theories. The structure of these algebras is still poorly understood.In this talk I shall consider finitely generated versions of q-W algebras. I shall show that q-W algebras belong to the class of the so-called Mickelsson algebras. They can be described in terms of certain conceptual analogues of projection operators introduced independently by Zhelobenko and by Asherova, Smirnov and Tolstoy in the course of the study of singular vectors in highest weight representations of complex semi-simple Lie algebras. This phenomenon does not take place for the usual W-algebras.

This talk is part of the Isaac Newton Institute Seminar Series series.

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