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SUMMARY:Enumerating defect zero blocks
DTSTART:20250909T084500Z
DTEND:20250909T094500Z
DTSTAMP:20260613T033000Z
UID:indico-event-14554@indico.math.cnrs.fr
DESCRIPTION:Speakers: Emily Norton (University of Kent)\n\nA staircase par
 tition cannot be tiled in such a way that upon removing a domino-shaped ti
 le from the staircase\, you still have a partition. We say that the stairc
 ase partition is a 2-core partition. The notion of an e-core partition is 
 similar\, but with e-ribbons in place of dominoes. The e-core partitions d
 escribe blocks in the representation theory of symmetric groups in positiv
 e characteristic\, but also rational Cherednik algebras and Hecke algebras
  at roots of unity. In the modular representation theory of the finite gen
 eral linear group\, the e-core partitions describe the unipotent blocks. 
  In 1996\, Granville and Ono proved that there exists an e-core partition 
 of every size n if e is at least 4 (when e is 2 or 3\, there are infinitel
 y many values of n without an e-core partition of size n). We may restate 
 Granville and Ono’s result as saying that in quantum characteristic at l
 east 4\, there exists a defect 0 unipotent block of GL(n\,q) for every nat
 ural number n. We may then ask if there is an analogue of this theorem for
  other finite classical groups\, for cyclotomic Hecke algebras at appropri
 ate parameters\, etc. This a project with Thomas Gerber.\n\nhttps://indico
 .math.cnrs.fr/event/14554/
LOCATION:Salle Fokko du Cloux (ICJ\, Université Lyon 1)
URL:https://indico.math.cnrs.fr/event/14554/
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