Modular representations and branching rules for affine and cyclotomic Yokonuma-Hecke algebras

Weideng Cui, Jinkui Wan

Published 2015-06-22Version 1

We establish an equivalence between a module category of the affine (resp. cyclotomic) Yokonuma-Hecke algebra $\widehat{Y}_{r,n}(q)$ (resp. $Y_{r,n}^{\lambda}(q)$) and its suitable counterpart for a direct sum of tensor products of affine Hecke algebras of type $A$ (resp. cyclotomic Hecke algebras). We then develop several applications of this result. The simple modules of affine Yokonuma-Hecke algebras and of their associated cyclotomic Yokonuma-Hecke algebras are classified over an algebraically closed field of characteristic $p=0$ or $(p,r)=1.$ The modular branching rules for these algebras are obtained, and they are further identified with crystal graphs of integrable modules for quantum affine algebras of type $A.$