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BEGIN:VEVENT
DTSTAMP:20220519T122913Z
DTSTART:20220524T120000Z
DTEND:20220524T130000Z
SUMMARY:Manchester Algebra Seminar - John Murray
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}n1ob-l30a4r
 2j-75v5ob
DESCRIPTION:Speaker: John Murray\n\nTitle: From the Alperin-McKay conject
 ure to Berstein-Zelevinsky Triangles\n\nAbstract: The McKay conjecture a
 sserts that a finite group has the same number of odd degree irreducible
  characters as the normalizers of its Sylow 2-subgroups. The Alperin-McK
 ay (A-M) conjecture generalizes this to the height-zero characters in th
 e 2-blocks of the group.\n\nIn his original paper\, McKay already showed
  that his conjecture holds for the finite symmetric groups $S_n$. In 201
 6\, Giannelli\, Tent and the speaker established a canonical bijection r
 ealising A-M for $S_n$\; the height-zero irreducible characters in a 2-b
 lock are naturally parametrized by tuples of hooks whose lengths are pow
 ers of 2\, and this parametrization is compatible with restriction to th
 e defect group.\n\nGiven a 2-block of $S_n$\, there is a corresponding 2
 -block of a certain maximal Young subgroup of $S_n$. It is an obvious qu
 estion to ask whether our canonical bijection is compatible with restric
 tion between these blocks.\n\nAttempting to prove this compatibility lea
 d me to a conjecture which asserts that certain differences of skew-Schu
 r functions are Schur positive. The corresponding skew-shapes have trian
 gular inner-shape\, but otherwise are independent of 2-block theory.\n\n
 I will describe my conjecture\, give positive evidence in its favour and
  outline a possible proof involving Berstein-Zelevinsky triangles.\n\n\n
 *subject to equipment and connection\n\nTea and biscuits 12:45 in the fo
 yer
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams\, Alan Turing Building\, Manchester
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