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DTSTART;TZID=America/Toronto:20250117T153000
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URL:/combinatorics-and-optimization/events/tutte-colloq
 uium-stephan-pfannerer-mittas
SUMMARY:Tutte colloquium-Stephan Pfannerer-Mittas
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE:A mystery group action and the mystery statis
 tic\n\nSPEAKER:\n Stephan Pfannerer-Mittas\n\nAFFILIATION:\n University of
  À¶Ý®ÊÓƵ\n\nLOCATION:\n MC 5501\n\nABSTRACT: In 2010\, B. Rhoades proved 
 that promotion on rectangular\nstandard Young tableaux together with the a
 ssociated fake-degree\npolynomial shifted by an appropriate power\, provid
 es an instance of\nthe cyclic sieving phenomenon. \n\nMotivated in part b
 y this result\, we show that we can expect a cyclic\nsieving phenomenon fo
 r _m_-tuples of standard Young tableaux of the\nsame shape and the _m_-t
 h power of the associated fake-degree\npolynomial\, for fixed _m_\, unde
 r mild and easily checked conditions.\nHowever\, we are unable to exhibit 
 an appropriate group action\nexplicitly.\nPut differently\, we determine i
 n which cases the _m_th tensor power\nof a character of the symmetric gro
 up carries a permutation\nrepresentation of the cyclic group. \nTo do so\
 , we use a method proposed by N. Amini and P. Alexandersson\,\nwhich amoun
 ts to establishing a bound on the number of border-strip\ntableaux. \n\nF
 inally\, 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 equidist
 ributed with the RSK-shape and invariant under\nrotation.\n\nThis is based
  on joint work with Per Alexandersson\, Martin Rubey and\nJoakim Uhlin.\n\
 n \n\n \n 
DTSTAMP:20250706T090600Z
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