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CATEGORIES:Algebra and Representation Theory Seminar
SUMMARY:Classifying the irreducible 2-modular modules of a
lternating groups and their double covers - John M
urray (Maynooth)
DTSTART;TZID=Europe/London:20180124T163000
DTEND;TZID=Europe/London:20180124T173000
UID:TALK96763AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/96763
DESCRIPTION:D. Benson used the notion of a spin regular partit
ion to describe all irreducible modules of alterna
ting groups over a field of characteristic 2. To d
etermine which of these modules are self-dual\, we
use a bijection\, due to M. Bressoud\, between th
e strict odd partitions and the spin regular parti
tions of an integer n.\n\nNow a 2-modular irreduci
ble module of a finite group has quadratic type if
its projective cover affords a quadratic geometry
. In recent joint work with R. Gow\, we showed tha
t the number of quadratic type irreducible modules
equals the number of strongly real 2-regular clas
ses. \n\nEuler's partition theorem is that the num
ber of odd partitions of n equals the number of st
rict partitions of n. Quite different bijective pr
oofs were discovered by Sylvester and Glaisher. In
order to determine the quadratic type of the irre
ducible modules of the double covers of alternatin
g groups we need a new correspondence between the
odd and strict partitions which combines propertie
s of the classical bijections.\n\nEuler's partitio
n theorem is that the number of odd partitions of
n equals the number of strict partitions of n. Qui
te different bijective proofs were discovered by S
ylvester and Glaisher. In order to determine the q
uadratic type of the irreducible modules of the do
uble covers of alternating groups we need a new co
rrespondence between the odd and strict partitions
which combines properties of the classical biject
ions.
LOCATION:MR12
CONTACT:Eugenio Giannelli
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