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 aspec...

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Bibliographic Details
Published in:arXiv.org 2021-05
Main Authors: Kontsevich, Maxim, Odesskii, Alexander
Format: Article
Language:English
Subjects:
Kernels
Mathematical analysis
Modules
Multiplication
Online Access:Get full text
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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:2331-8422
DOI:10.48550/arxiv.2105.04238