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SUMMARY:e-Cores and e-Weights of Multipartitions and Blocks of Ariki-Koike
  Algebras - Kai Meng Tan\, National University of Singapore
DTSTART:20240528T153000Z
DTEND:20240528T163000Z
UID:TALK216727@talks.cam.ac.uk
CONTACT:Adam Jones
DESCRIPTION:The Uglov map sends a multipartition (with an associated multi
 charge) to a partition. Using this Uglov map\, I will show how one can use
  the e-abacus to define the e-core (which is a partition) and the e-weight
  (which is a non-negative integer) of a multipartition associated to a mul
 ti-e-residue.\nThis combinatorial definition of $e$-weight coincides with 
 the definition first introduced by Fayers. Furthermore\, two Specht module
 s of an Ariki-Koike algebra lie in the same block if and only if they are 
 labelled by multipartitions with the same e-core and the same e-weight. Th
 is thus provides a characterisation of the blocks of Ariki-Koike algebras 
 that is analogous to that of Iwahori-Hecke algebras. If time allows\, I wi
 ll discuss the implications of these results for Scopes's equivalences for
  the blocks of Ariki-Koike algebras\, as well as suggest a definition of R
 ouquier blocks of Ariki-Koike algebras that is different from Lyle's\, but
  is perhaps more natural.
LOCATION:MR19 (Potter Room\, Pavilion B)\, CMS
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