Cyclic sieving phenomenon on dominant maximal weights over affine Kac-Moody algebras
- 주제(키워드) Affine Kac-Moody algebra , Cyclic sieving phenomenon , Dominant maximal weight
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- OA유형 Green Submitted
- 발행기관 Academic Press Inc.
- 발행년도 2020
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000172274
- 본문언어 영어
- Published As https://dx.doi.org/10.1016/j.aim.2020.107336
초록/요약
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.
more