Multiplication kernels

We introduce the notion of multiplication kernels of birational and D -module type and give various examples. We also introduce the notion of a semi-classical multiplication kernel associated with an integrable system and discuss its quantization. Finally, we discuss geometric and algebraic aspects...

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Bibliographic Details
Published in:Letters in mathematical physics 2021-12, Vol.111 (6), Article 152
Main Authors: Kontsevich, Maxim, Odesskii, Alexander
Format: Article
Language:English
Subjects:
Boris Dubrovin Memorial Issue
Complex Systems
Geometry
Group Theory and Generalizations
Kernels
Mathematical analysis
Mathematical and Computational Physics
Modules
Multiplication
Physics
Physics and Astronomy
Theoretical
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Summary:We introduce the notion of multiplication kernels of birational and D -module type and give various examples. We also introduce the notion of a semi-classical multiplication kernel associated with an integrable system and discuss its quantization. Finally, we discuss geometric and algebraic aspects of method of separation of variables and describe hypothetically a cyclic D -module for the generalized multiplication kernels for Hitchin systems for groups GL r .
ISSN:0377-9017
1573-0530
DOI:10.1007/s11005-021-01491-1