Abstract
We study algebras constructed by quantum Hamiltonian reduction associated with symplectic quotients of symplectic vector spaces, including deformed preprojective algebras, symplectic reection algebras (rational Cherednik algebras), and quantization of hypertoric varieties introduced by Musson and Van den Bergh in [MVdB]. We determine BRST cohomologies associated with these quantum Hamiltonian reductions. To compute these BRST cohomologies, we make use of the method of deformation quantization (DQ-algebras) and F-action studied by Kashiwara and Rouquier in [KR], and Gordon and Losev in [GL].
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Dedicated to Professor Tetsuji Miwa on the occasion of his retirement
*This work was financially supported by the Government of the Russian Federation in the framework of the “Road Map” Programme 5/100 of National Research University “Higher School of Economics.” The author was partially supported by Grant-in-Aid for Young Scientist (B) 21740013, Japan Society for the Promotion of Science and the GCOE Program “Fostering Top Leaders in Mathematics”, Kyoto University. This work was partially supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MEST)(2011–0027952).
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KUWABARA, T. BRST COHOMOLOGIES FOR SYMPLECTIC REFLECTION ALGEBRAS AND QUANTIZATIONS OF HYPERTORIC VARIETIES. Transformation Groups 20, 437–461 (2015). https://doi.org/10.1007/s00031-015-9314-0
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DOI: https://doi.org/10.1007/s00031-015-9314-0