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Quantizing Mishchenko-Fomenko subalgebras for centralizers via affine $ W$-algebras


Authors: T. Arakawa and A. Premet
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 78 (2017), vypusk 2.
Journal: Trans. Moscow Math. Soc. 2017, 217-234
MSC (2010): Primary 17B35, 17B08, 17B20, 17B69
DOI: https://doi.org/10.1090/mosc/264
Published electronically: December 1, 2017
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Abstract: We use affine $ W\!$-algebras to quantize Mishchenko-Fomenko subalgebras for centralizers of nilpotent elements in finite dimensional simple Lie algebras under certain assumptions that are satisfied for all cases in type $ \mathrm {A}$ and all minimal nilpotent cases outside type $ \mathrm {E}_8$.


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Additional Information

T. Arakawa
Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Japan
Email: arakawa@kurims.kyoto-u.ac.jp

A. Premet
Affiliation: School of Mathematics, The University of Manchester, United Kingdom
Email: alexander.premet@manchester.ac.uk

DOI: https://doi.org/10.1090/mosc/264
Keywords: Mishchenko--Fomenko subalgebras, vertex algebras, affine $W$-algebras
Published electronically: December 1, 2017
Additional Notes: The first author was partially supported by JSPS KAKENHI Grants (#25287004 and #26610006).
The second author was supported by the Leverhulme Trust (Grant RPG-2013–293).
Dedicated: Dedicated to Ernest Borisovich Vinberg for his $80$th birthday
Article copyright: © Copyright 2017 T.Arakawa, A.Premet

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