New applications of the Reflection Equation Algebras

The REA are treated to be $q$-analogs of the enveloping algebras $U(gl(N))$. In particular, each of them has a representation category similar to that of $U(gl(N))$. I plan to exhibit new applications of these algebras:
1. $q$-Capelli formula
2. $q$-Frobenius formula
3. $q$-Casimir and $q$-cut-and-join operators