Traces on finite W-algebras
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Etingof_Traces on (arxiv).pdf
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147.9 KB
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Author(s)
Etingof, Pavel I.
Schedler, Travis
Date Issued
June 2010
Journal
Transformation Groups
Publisher
Springer-Verlag
Citation
Etingof, Pavel, and Travis Schedler. “Traces on Finite W-algebras.” Transformation Groups 15.4 (2010): 843–850. Web. 11 Apr. 2012.
Version
Author's final manuscript
Abstract
We compute the space of Poisson traces on a classical W-algebra, i.e., linear functionals invariant under Hamiltonian derivations. Modulo any central character, this space identifies with the top cohomology of the corresponding Springer fiber. As a consequence, we deduce that the zeroth Hochschild homology of the corresponding quantum W-algebra modulo a central character identifies with the top cohomology of the corresponding Springer fiber. This implies that the number of irreducible finite-dimensional representations of this algebra is bounded by the dimension of this top cohomology, which was established earlier by C. Dodd using reduction to positive characteristic. Finally, we prove that the entire cohomology of the Springer fiber identifies with the so-called Poisson-de Rham homology (defined previously by the authors) of the centrally reduced classical W-algebra.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1007/s00031-010-9103-8
