English

Cellularity of cyclotomic Yokonuma-Hecke algebras

Representation Theory 2016-08-22 v7

Abstract

We first give a direct proof of a basis theorem for the cyclotomic Yokonuma-Hecke algebra Yr,nd(q).Y_{r,n}^{d}(q). Our approach follows Kleshchev's, which does not use the representation theory of Yr,nd(q),Y_{r,n}^{d}(q), and so it is very different from that of [ChP2]. We also present two applications. Then we prove that the cyclotomic Yokonuma-Hecke algebra Yr,nd(q)Y_{r,n}^{d}(q) is cellular by constructing an explicit cellular basis, and show that the Jucys-Murphy elements for Yr,nd(q)Y_{r,n}^{d}(q) are JM-elements in the abstract sense. In the appendix, we shall develop the fusion procedure for Yr,nd(q).Y_{r,n}^{d}(q).

Keywords

Cite

@article{arxiv.1506.07321,
  title  = {Cellularity of cyclotomic Yokonuma-Hecke algebras},
  author = {Weideng Cui},
  journal= {arXiv preprint arXiv:1506.07321},
  year   = {2016}
}

Comments

Fusion procedures of cyclotomic Y-H algebras are added in the appendix. In the arXiv:1405.6441, we define and study Yokonuma-Schur algebras and cyclotomic analogues. arXiv admin note: text overlap with arXiv:1208.4884; text overlap with arXiv:1506.00715 by other authors