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 $(\mathbb{Z}\mathrm{/}r\mathbb{Z})\wr {\mathfrak{S}}_n$ over an algebraically closed field of characteristic $p>0$ such that $p$ does not divide $r$.