q-difference intertwining operators for $U_q(sl(n))$: general setting and the case $n=3$

Abstract

We construct representations $\hatπ_{\br}$ of the quantum algebra $U_q(sl(n))$ labelled by $n-1$ complex numbers $r_i$ and acting in the space of formal power series of $n(n-1)/2$ non-commuting variables. These variables generate a flag manifold of the matrix quantum group $S{L}_q(n)$ which is dual to $U_q(sl(n))$. The conditions for reducibility of $\hatπ_{\br}$ and the procedure for the construction of the $q$ - difference intertwining operators are given. The representations and $q$ - difference intertwining operators are given in the most explicit form for $n=3$. In the Note Added some general results for arbitrary $n$ are given.

24 pages; v2 includes Note Added published in J.Phys. A27 (1994), references updated

Cited by in corpus (12)

• Invariant Differential Operators for Non-Compact Lie Groups: Parabolic Subalgebras
• Exceptional Lie Algebra $E_{7(-25)}$ (Multiplets and Invariant Differential Operators)
• Quantum flag manifolds, quantum symmetric spaces and their associated universal K-matrices
• Quantum Heisenberg Group and Algebra: Contraction, Left and Right Regular Representations
• On Fock Space Representations of quantized Enveloping Algebras related to Non-Commutative Differential Geometry
• q-Conformal Invariant Equations and q-Plane Wave Solutions
• Left Regular Representation of $s{l}_q(3)$: Reduction and Intertwiners
• Induced Representations of Quantum Kinematical Algebras and Quantum Mechanics
• Representations of Quantum Bicrossproduct Algebras
• q-Plane Wave Solutions of q-Weyl gravity
• Induced representations of quantum kinematical algebras
• Classification of Invariant Differential Operators for Non-Compact Lie Algebras via Parabolic Relations