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DTSTART:20240310T070000
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DTSTART:20241103T060000
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DTSTART;TZID=America/Toronto:20250117T153000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/tutte-colloq
 uium-stephan-pfannerer-mittas
SUMMARY:Tutte colloquium-Stephan Pfannerer-Mittas
CLASS:PUBLIC
DESCRIPTION:TITLE:A mystery group action and the mystery statistic\n\nSPEAK
 ER:\n Stephan Pfannerer-Mittas\n\nAFFILIATION:\n University of Waterloo\n\
 nLOCATION:\n MC 5501\n\nABSTRACT: In 2010\, B. Rhoades proved that promoti
 on on rectangular\nstandard Young tableaux together with the associated fa
 ke-degree\npolynomial shifted by an appropriate power\, provides an instan
 ce of\nthe cyclic sieving phenomenon. \n\nMotivated in part by this resul
 t\, we show that we can expect a cyclic\nsieving phenomenon for _m_-tuple
 s of standard Young tableaux of the\nsame shape and the _m_-th power of 
 the associated fake-degree\npolynomial\, for fixed _m_\, under mild and e
 asily checked conditions.\nHowever\, we are unable to exhibit an appropria
 te group action\nexplicitly.\nPut differently\, we determine in which case
 s the _m_th tensor power\nof a character of the symmetric group carries a
  permutation\nrepresentation of the cyclic group. \nTo do so\, we use a m
 ethod proposed by N. Amini and P. Alexandersson\,\nwhich amounts to establ
 ishing a bound on the number of border-strip\ntableaux. \n\nFinally\, we 
 apply our results to the invariant theory of tensor powers\nof the adjoint
  representation of the general linear group. In\nparticular\, we prove the
  existence of a statistic on permutations\,\nwhich is equidistributed with
  the RSK-shape and invariant under\nrotation.\n\nThis is based on joint wo
 rk with Per Alexandersson\, Martin Rubey and\nJoakim Uhlin.\n\n \n\n 
DTSTAMP:20260405T062120Z
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