Multiplication kernels
Maxim Kontsevich, Alexander Odesskii

TL;DR
This paper introduces multiplication kernels in the context of birational and D-modules, explores their semi-classical and quantum aspects, and discusses their role in integrable systems and separation of variables.
Contribution
It presents new concepts of multiplication kernels and their semi-classical and quantized forms, linking algebraic geometry with integrable systems and D-module theory.
Findings
Examples of multiplication kernels provided
Discussion of quantization of semi-classical kernels
Hypothetical cyclic D-module for Hitchin systems
Abstract
We introduce the notion of multiplication kernels of birational and -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 -module for the generalized multiplication kernels for Hitchin systems for groups .
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