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 \( \mathfrak{g} \). 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.
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SEVOSTYANOV, A. THE STRUCTURE OF Q-W ALGEBRAS. Transformation Groups 25, 279–304 (2020). https://doi.org/10.1007/s00031-019-09533-8
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DOI: https://doi.org/10.1007/s00031-019-09533-8