Séminaire Lotharingien de Combinatoire, 84B.29 (2020), 12 pp.

Young-Hun Kim, Se-jin Oh and Young-Tak Oh

Cyclic Sieving Phenomenon on Dominant Maximal Weights

Abstract. Dominant maximal weights are significant objects in the representation theory of affine Kac-Moody algebras. We construct a (bi)cyclic sieving phenomenon on the union of dominant maximal weights for highest weight modules over affine Kac-Moody algebras in a way not depending on types, ranks and levels. Exploiting this phenomenon, we derive closed and recursive formulae for the number of dominant maximal weights for every highest weight module and observe level-rank duality on the cardinalities. We also observe interesting interrelations among the recursive formulae of classical affine Kac-Moody algebras.

Received: November 20, 2019. Accepted: February 20, 2020. Final version: April 30, 2020.

The following versions are available: