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Cyclic sieving phenomenon on dominant maximal weights over affine Kac-Moody algebras
Title
Cyclic sieving phenomenon on dominant maximal weights over affine Kac-Moody algebras
Authors
Kim Y.-H.
;
Oh S.-J.
;
Oh Y.-T.
Ewha Authors
오세진
SCOPUS Author ID
오세진
Issue Date
2020
Journal Title
Advances in Mathematics
ISSN
0001-8708
Citation
Advances in Mathematics vol. 374
Keywords
Affine Kac-Moody algebra
;
Cyclic sieving phenomenon
;
Dominant maximal weight
Publisher
Academic Press Inc.
Indexed
SCIE; SCOPUS
Document Type
Article
Abstract
We construct a (bi)cyclic sieving phenomenon on the union of dominant maximal weights for level ℓ highest weight modules over an affine Kac-Moody algebra with exactly one highest weight being taken for each equivalence class, in a way not depending on types, ranks and levels. In order to do that, we introduce S-evaluation on the set of dominant maximal weights for each highest modules, and generalize Sagan's action in [17] by considering the datum on each affine Kac-Moody algebra. As consequences, we obtain closed and recursive formulae for cardinality of the number of dominant maximal weights for every highest weight module and observe level-rank duality on the cardinalities. © 2020 Elsevier Inc.
DOI
10.1016/j.aim.2020.107336
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