The structure of Q-W algebras

Alexey Sevastyanov* (Corresponding Author)

*Corresponding author for this work

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We suggest two explicit descriptions of the Poisson q-W algebras which are Poisson algebras of regular functions on certain algebraic group analogues of the Slodowy transversal slices to adjoint orbits in a complex semisimple Lie algebra g. To obtain the first description we introduce certain projection operators which are analogous to the quasi–classical versions of the so–called Zhelobenko and extremal projection operators. As a byproduct we obtain some new formulas for natural coordinates on Bruhat cells in algebraic groups.
Original languageEnglish
Pages (from-to)279–304
Number of pages26
JournalTransformation Groups
Issue number1
Early online date11 May 2019
Publication statusPublished - Mar 2020


  • Algebraic group
  • Transversal slice
  • Poisson manifold


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