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SUMMARY:Pavlo Pylyavskyy (University of Minnesota)
DTSTART:20221102T130000Z
DTEND:20221102T143000Z
DTSTAMP:20260423T021111Z
UID:algsjtu/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/algsjtu/1/">
 Crystal Invariant Theory</a>\nby Pavlo Pylyavskyy (University of Minnesota
 ) as part of SJTU algebra seminar\n\n\nAbstract\nAbstract: Berenstein and 
 Kazhdan have introduced a birational lifting of\nKashiwara's crystals\, ca
 lled geometric crystals. Their theory gives rise to\nfour families of oper
 ators acting on the space of complex $m \\times n$\nmatrices\, two acting 
 by geometric crystal operators and two acting by\ngeometric R-matrices. Th
 ese actions can be viewed as "crystal analogues" of\nthe usual actions of 
 $GL_m$ and $GL_n$ - and their subgroups $S_m$ and\n$S_n$ - on the polynomi
 al ring in $m \\times n$ variables. Many important\nfunctions in the theor
 y of geometric crystals are invariants of one or more\nof those actions. T
 he examples include $\\epsilon$ and $\\phi$ functions\,\nenergy function\,
  decoration function\, insertion and recording tableaux of\nNoumi-Yamada g
 eometric RSK\, central charge\, etc. We study generators of the\ninvariant
 s of one or more of the families of operators\, and obtain new\nformulas f
 or the important functions by writing them in terms of those\ngenerators. 
 The talk is based on joint work with Ben Brubaker\, Gabe\nFrieden\, Travis
  Scrimshaw\, and Thomas Lam.\n\nZoom meeting ID: 927 9300 3904\nPassword: 
 909921\n
LOCATION:https://researchseminars.org/talk/algsjtu/1/
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