R-matrix and Mickelsson algebras for orthosymplectic quantum groups

TL;DR

This paper constructs explicit generators for Mickelsson algebras associated with orthogonal and symplectic quantum groups using R-matrices, advancing understanding of their algebraic structure.

Contribution

It provides an explicit construction of Mickelsson algebra generators for orthosymplectic quantum groups using R-matrices and Chevalley generators.

Findings

Explicit generators of Mickelsson algebras are constructed.

The approach utilizes the R-matrix of quantum groups.

Results facilitate further study of quantum group representations.

Abstract

Let $\g$ be a complex orthogonal or symplectic Lie algebra and $\g'\subset \g$ the Lie subalgebra of rank $\rk \g'=\rk \g-1$ of the same type. We give an explicit construction of generators of the Mickelsson algebra $Z_q(\g,\g')$ in terms of Chevalley generators via the R-matrix of $U_q(\g)$.