Abacus models for parabolic quotients of affine Weyl groups

Details Abacus models for parabolic quotients of affine Weyl groups Abacus models for parabolic quotients of affine Weyl groups

2011-05-26

arxiv.org/abs/1105.5333v2

Mathematics

Combinatorics

28 pages, To appear, Journal of Algebra. Version 2: Updated with referee's comments

Scientific paper

We introduce abacus diagrams that describe minimal length coset representatives in affine Weyl groups of types B, C, and D. These abacus diagrams use a realization of the affine Weyl group of type C due to Eriksson to generalize a construction of James for the symmetric group. We also describe several combinatorial models for these parabolic quotients that generalize classical results in affine type A related to core partitions.

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