We consider representations of the Ariki-Koike algebra, a q-deformation of the group algebra of the complex reflection group Cr ≀ Sn. The representations of this algebra are naturally indexed by multipartitions of n. We examine blocks of the Ariki-Koike algebra, in an attempt to generalise the combinatorial representation theory of the Iwahori-Hecke algebra. In particular, we prove a sufficient condition such that restriction of modules leads to a natural correspondence between the multipartitions of n whose Specht modules belong to a block B and those of n-δi(B) whose Specht modules belong to the block B‘, obtained from B applying a Scopes equivalence.
This video was produced by the Okinawa Institute of Science and Technology, as part of their OIST Representation Theory Seminar series.
