Abstract
We consider the representation theory of the Ariki-Koike algebra, a q-deformation of the group algebra of the complex reflection group Cr≀Sn. We define the addition of a runner full of beads for the abacus display of a multipartition and investigate some combinatorial properties of this operation. We focus our attention on the v-decomposition numbers, i.e. the polynomials arising from the Fock space representation of the quantum group Uv(slˆe). Using Fayers' LLT-type algorithm for Ariki-Koike algebras, we relate v-decomposition numbers for different values of e for the class of e-multiregular multipartitions, by adding a full runner of beads to each component of the abacus displays for the labelling multipartitions.
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