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SUMMARY:Joel Kamnitzer (University of Toronto)
DTSTART:20210930T185000Z
DTEND:20210930T195000Z
DTSTAMP:20260423T005850Z
UID:GPRTatNU/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GPRTatNU/31/
 ">Monodromy of eigenvectors for trigonometric Gaudin algebras</a>\nby Joel
  Kamnitzer (University of Toronto) as part of Geometry\, Physics\, and Rep
 resentation Theory Seminar\n\n\nAbstract\nConsider a tensor product of rep
 resentations of a semisimple Lie algebra g. The Gaudin algebra is a commut
 ative algebra which acts on this tensor product\, commuting with the actio
 n of g. This algebra depends on a parameter which lives in the moduli spac
 e of marked genus 0 curves. In previous work\, we studied the monodromy of
  eigenvectors for this algebra as the parameter varies in the real locus o
 f this space. In new work in-progress\, we consider trigonometric Gaudin a
 lgebras\, which act on the same vector space (but do not commute with the 
 g-action). We see that this leads to the action of the affine cactus group
 \, and we describe the action of this group combinatorially using crystals
 . I will also describe the (conjectural) relation between trigonometric Ga
 udin algebras and the quantum cohomology of affine Grassmannian slices.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/31/
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