OIST Representation Theory Seminar

Alice Dell'Arciprete, University of East Anglia

Title: Scopes equivalence for blocks of Ariki-Koike algebras

Abstract: We consider representations of the Ariki-Koike algebra, a \(q\)-deformation of the group algebra of the complex reflection group \(C_r \wr S_n\). 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 \(n-\delta_i(B)\) whose Specht modules belong to the block \(B'\), obtained from \(B\) applying a Scopes' equivalence.

Zoom info can be found on the seminar webpage.