The structure of Q-W algebras

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Abstract

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
Number of pages20
JournalTransformation Groups
Early online date11 May 2019
DOIs
Publication statusE-pub ahead of print - 11 May 2019

Fingerprint

W-algebras
Projection Operator
Algebraic Groups
Semisimple Lie Algebra
Slice
Siméon Denis Poisson
Orbit
Analogue
Cell

Keywords

  • Algebraic group
  • Transversal slice
  • Poisson manifold

Cite this

The structure of Q-W algebras. / Sevastyanov, Alexey.

In: Transformation Groups, 11.05.2019.

Research output: Contribution to journalArticle

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