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SUMMARY:Matthew Fayers (Queen Mary University of London)
DTSTART:20210112T073000Z
DTEND:20210112T083000Z
DTSTAMP:20260423T021306Z
UID:OISTRTS/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OISTRTS/8/">
 The Mullineux map</a>\nby Matthew Fayers (Queen Mary University of London)
  as part of OIST representation theory seminar\n\n\nAbstract\nIn character
 istic p\, the simple modules for the symmetric group \\(S_n\\) are the Jam
 es modules \\(D^\\lambda\\)\, labelled by p-regular partitions of n. If we
  let \\(sgn\\) denote the 1-dimensional sign module\, then for any p-regul
 ar \\(\\lambda\\)\, the module \\(D^\\lambda\\otimes sgn\\) is also a simp
 le module. So there is an involutory bijection \\(m_p\\) on the set of p-r
 egular partitions such that \\(D^\\lambda\\otimes sgn=D^{m_p(\\lambda)}\\)
 . The map \\(m_p\\) is called the Mullineux map\, and an important problem
  is to describe \\(m_p\\) combinatorially. There are now several known sol
 utions to this problem. I will describe the history of this problem and ex
 plain the known combinatorial solutions\, and then give a new solution bas
 ed on crystals and regularisation.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/8/
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