R-matrix and Mickelsson algebras for orthosymplectic quantum groups

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 $U_q(\g)$.

12 pages, no figures; a minor correction on p.7

References in corpus (2)

• On representations of quantum conjugacy classes of GL(n)
• q-Analog of Gelfand-Graev Basis for the Noncompact Quantum Algebra U_q(u(n,1))

Cited by in corpus (2)

• Diagonal reduction algebra for $\mathfrak{osp}(1|2)$
• Symplectic Differential Reduction Algebras and Generalized Weyl Algebras