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SUMMARY:Alexander Shapiro (Notre Dame)
DTSTART:20210325T185000Z
DTEND:20210325T195000Z
DTSTAMP:20260423T022931Z
UID:GPRTatNU/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GPRTatNU/22/
 ">Cluster realization of spherical DAHA</a>\nby Alexander Shapiro (Notre D
 ame) as part of Geometry\, Physics\, and Representation Theory Seminar\n\n
 \nAbstract\nSpherical subalgebra of Cherednik's double affine Hecke algebr
 a of type A admits a polynomial representation in which its generators act
  via elementary symmetric functions and Macdonald operators. Recognizing t
 he elementary symmetric functions as eigenfunctions of quantum Toda Hamilt
 onians\, and applying (the inverse of) the Toda spectral transform\, one o
 btains a new representation of spherical DAHA. In this talk\, I will discu
 ss how this new representation gives rise to an injective homomorphism fro
 m the spherical DAHA into a quantum cluster algebra in such a way that the
  action of the modular group on the former is realized via cluster transfo
 rmations. The talk is based on a joint work in progress with Philippe Di F
 rancesco\, Rinat Kedem\, and Gus Schrader.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/22/
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