Calibrated representations of affine Yokonuma-Hecke algebras

Inspired by the work [Ra1], we directly give a complete classification of irreducible calibrated representations of affine Yokonuma-Hecke algebras $widehat{Y}_{r,n}(q)$ over $mathbb{C},$ which are indexed by $r$-tuples of placed skew shapes. We then develop several applications of this result. In the appendix, inspired by [Ru], we classify and construct irreducible completely splittable representations of degenerate affine Yokonuma-Hecke algebras $D_{r,n}$ and the wreath product $(mathbb{Z}/rmathbb{Z})wr mathfrak{S}_{n}$ over an algebraically closed field of characteristic $p> 0$ such that $p$ does not divide $r$.