BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:John Murray (Maynooth University)
DTSTART:20220322T073000Z
DTEND:20220322T083000Z
DTSTAMP:20260423T021250Z
UID:OISTRTS/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OISTRTS/29/"
 >A Schur-positivity conjecture inspired by the Alperin-Mckay conjecture</a
 >\nby John Murray (Maynooth University) as part of OIST representation the
 ory seminar\n\n\nAbstract\nThe McKay conjecture asserts that a finite grou
 p has the same number of odd degree irreducible characters as the normaliz
 er of a Sylow 2-subgroup. The Alperin-McKay (A-M) conjecture generalizes t
 his to the height-zero characters in 2-blocks.\n\nIn his original paper\, 
 McKay already showed that his conjecture holds for the finite symmetric gr
 oups S_n. In 2016\, Giannelli\, Tent and the speaker established a canonic
 al bijection realising A-M for S_n\; the height-zero irreducible character
 s in a 2-block are naturally parametrized by tuples of hooks whose lengths
  are certain powers of 2\, and this parametrization is compatible with res
 triction to an appropriate 2-local subgroup.\n\nNow corresponding to a 2-b
 lock of the symmetric group S_n\, there is a 2-block of a maximal Young su
 bgroup of S_n of the same weight. An obvious question is whether our canon
 ical bijection is compatible with restriction of height-zero characters be
 tween these blocks.\n\nAttempting to prove this compatibility lead me to f
 ormulate a conjecture asserting the Schur-positivity of certain difference
 s of skew-Schur functions. The corresponding skew-shapes have triangular i
 nner-shape\, but otherwise do not refer to the 2-modular theory. I will de
 scribe my conjecture and give positive evidence in its favour.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/29/
END:VEVENT
END:VCALENDAR