Appears in collection : Combinatorics and Arithmetic for Physics: special days 2023

Reflection Equation Algebras (without parameters) are very remarkable objects. They admit introducing q-analogs of certain symmetric functions and quantum versions of some classical formulae of combinatorics: Capelli, Frobenius and others. Also, they admit introducing quantum analogs of differential operators. I plan to introduce some quantum invariant differential operators and to exhibit their properties.