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Duality and Integrability in Macdonald Theory December 02, 2021 (02:00 PM PST - 03:00 PM PST)
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Location: MSRI: Simons Auditorium, Online/Virtual
Speaker(s) Rinat Kedem (University of Illinois at Urbana-Champaign)
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Duality And Integrability In Macdonald Theory


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Using the notion of duality, or bispectrality, in Macdonal theory, can derive the Pieri operators from the eigenvalue equation for Macdonald-Koornwinder operators. These commuting difference  operators, in the q-Whittaker limit, can be regarded as q-difference relativistic Toda Hamiltonians for some root systems, and their eigenfunctions as q-Whittaker functions. One can use the SL_2(Z)-action on the spherical DAHA, acting on the Macdonald or Koornwinder operators, to obtain a set of operators which, in the limit, act as raising operators for q-Whittaker functions. [Joint work with P. Di Francesco]

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Duality And Integrability In Macdonald Theory