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International Conference "Fields & Strings 2025"
December 5, 2025 15:30, Moscow, Steklov Mathematical Institute


Integrable System associated with genus 2 Macdonald polynomials

Shamil Shakirov

Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow



Abstract: We present an interesting quantum integrable system with 3 degrees of freedom. Eigenfunctions of this system are new special functions — genus 2 Macdonald polynomials. This name is justified because these polynomials admit an action of genus 2 mapping class group, generalizing the $SL(2,\mathbb{Z})$ action for ordinary Macdonald polynomials. Using this integrable system, we conjecture certain new knot invariants.

Language: English


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