Star and weak star irreducible fully commutative elements in Coxeter groups of affine types $\tilde{B}$ and $\tilde{D}$

Riccardo Biagioli, Luca Costantini, Elisa Sasso

The star operation, originally introduced by Kazhdan and Lusztig, was later specialized by Ernst to the so-called weak star reduction on the set of fully commutative elements of a…