Modular representations and branching rules for affine and cyclotomic Yokonuma-Hecke algebras
We give an equivalence between a module category of the affine Yokonuma-Hecke algebra (associated with the group $\mathbb{Z}/r\mathbb{Z}$) and its suitable counterpart for a direct sum of tensor products of affine Hecke algebras of type $A$. We then develop several applications of this result. In particular, the simple modules of the affine Yokonuma-Hecke algebra and of its associated cyclotomic algebra are classified over an algebraically closed field of characteristic $p$ when $p$ does not divide $r$. The modular branching rules for these algebras are obtained, and they are further identified with crystal graphs of integrable modules for quantum affine algebras.