Ruijsenaars spectral transform

Abstract: Recent success in the study of Baxter $Q$ operators in Ruijsenaars hyperbolic system led to establishing, besides of bispectral duality, of the duality concerning reflection of the coupling constant. It also gives a way to prove orthogonality and completeness of the wave functions. The corresponding integral transform, defined for complex valued parameters, can be regarded as a generalization of Laplace transform. We prove an analog of classical inversion formula and apply it for establishing $L_2$ isomorphisms of Ruijsenaars spectral transform in 4 regimes of unitarity of the system.

mathematical physicsdynamical systemsquantum algebrarepresentation theorysymplectic geometry

Audience: general audience

( video )

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BIMSA Integrable Systems Seminar

Series comments: The aim is to bring together experts in integrable systems and related areas of theoretical and mathematical physics and mathematics. There will be research presentations and overview talks.

Audience: Graduate students and researchers interested in integrable systems and related mathematical structures, such as symplectic and Poisson geometry and representation theory.

The zoom link will be distributed by mail, so please join the mailing list if you are interested in attending the seminar.

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