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SUMMARY:The image of the Specht module under the inverse Schur functor - E
 oghan McDowell (Royal Holloway University of London)
DTSTART:20201104T093000Z
DTEND:20201104T103000Z
UID:TALK153601@talks.cam.ac.uk
CONTACT:Stacey Law
DESCRIPTION:The Schur functor and its inverses give an important connectio
 n\nbetween the representation theories of the symmetric group and the gene
 ral\nlinear group. Kleshchev and Nakano proved in 2001 that when the\nchar
 acteristic of the field is at least 5\, the image of the Specht module\nun
 der the inverse Schur functor is isomorphic to the dual Weyl module. In\nt
 his talk I will address what happens in characteristics 2 and 3: in\nchara
 cteristic 3\, the isomorphism holds\, and I will give an elementary\nproof
  of this fact which covers also all characteristics other than 2\; in\ncha
 racteristic 2\, the isomorphism does not hold for all Specht modules\, and
 \nI will classify those for which it does. Our approach is with Young\ntab
 leaux\, tabloids and Garnir relations.
LOCATION:by zoom
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