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Title:
Deformed Ruijsenaars operators and elliptic hypergeometric functions
Speaker:
Abstract:
The Ruijsenaars operators are a commuting family of difference operators with elliptic coefficients, which define an integrable system of relativistic quantum particles. Through the work of Chalykh, Feigin, Silantyev, Veselov and others, it has become apparent that even more general "deformed" or "super" operators exist. We will describe how to obtain the main properties of such operators in a direct way, which works also in the elliptic setting. In particular, we can prove that the deformed elliptic Ruijsenaars model is integrable, which has until now been an unsolved problem. Our results are intimately related to identities for elliptic hypergeometric series. The talk is based on joint work (Comm. Math. Phys., 2022) with Martin Hallnäs, Edwin Langmann and Masatoshi Noumi.
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