Bijective projections on parabolic quotients of affine Weyl groups
Document Type
Journal Article
Role
Author
Published In
Journal of Algebraic Combinatorics
Publisher
Springer
Volume
41
First Page
911
Last Page
948
Publication Date
10-18-2014
Abstract
Affine Weyl groups and their parabolic quotients are used extensively as indexing sets for objects in combinatorics, representation theory, algebraic geometry, and number theory. Moreover, in the classical Lie types we can conveniently realize the elements of these quotients via intuitive geometric and combinatorial models such as abaci, alcoves, coroot lattice points, core partitions, and bounded partitions. In [2], Berg et al. described a bijection between n-cores with first part equal to k and (n −1)- cores with first part less than or equal to k, and they interpret this bijection in terms of these other combinatorial models for the quotient of the affine symmetric group by
Keywords
Core partition, Abacus diagram, Root system, Hyperplane arrangement, Alcove walk, Affine Weyl group, Affine Grassmannian
Suggested Citation
Beazley, E., Nichols, M., Park, M.H. et al. Bijective projections on parabolic quotients of affine Weyl groups. J Algebr Comb 41, 911–948 (2015). https://doi.org/10.1007/s10801-014-0559-9
