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SUMMARY:Classifying the irreducible 2-modular modules of alternating group
 s and their double covers - John Murray (Maynooth)
DTSTART:20180124T163000Z
DTEND:20180124T173000Z
UID:TALK96763@talks.cam.ac.uk
CONTACT:Eugenio Giannelli
DESCRIPTION:D. Benson used the notion of a spin regular partition to descr
 ibe all irreducible modules of alternating groups over a field of characte
 ristic 2. To determine which of these modules are self-dual\, we use a bij
 ection\, due to M. Bressoud\, between the strict odd partitions and the sp
 in regular partitions of an integer n.\n\nNow a 2-modular irreducible modu
 le of a finite group has quadratic type if its projective cover affords a 
 quadratic geometry. In recent joint work with R. Gow\, we showed that the 
 number of quadratic type irreducible modules equals the number of strongly
  real 2-regular classes. \n\nEuler's partition theorem is that the number 
 of odd partitions of n equals the number of strict partitions of n. Quite 
 different bijective proofs were discovered by Sylvester and Glaisher. In o
 rder to determine the quadratic type of the irreducible modules of the dou
 ble covers of alternating groups we need a new correspondence between the 
 odd and strict partitions which combines properties of the classical bijec
 tions.\n\nEuler's partition theorem is that the number of odd partitions o
 f n equals the number of strict partitions of n. Quite different bijective
  proofs were discovered by Sylvester and Glaisher. In order to determine t
 he quadratic type of the irreducible modules of the double covers of alter
 nating groups we need a new correspondence between the odd and strict part
 itions which combines properties of the classical bijections.
LOCATION:MR12
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