Left Regular Representation of $s{l}_q(3)$: Reduction and Intertwiners

Abstract

Reduction of the left regular representation of quantum algebra $s{l}_q(3)$ is studied and ~$q$-difference intertwining operators are constructed. The irreducible representations correspond to the spaces of local sections of certain line bundles over the q-flag manifold.

17 pages. References added typographical errors corrected

References in corpus (7)

• Symmetries of quantum spaces. Subgroups and quotient spaces of quantum $SU(2)$ and $SO(3)$ groups
• Quantum group gauge theory on quantum spaces
• q-difference intertwining operators for $U_q(sl(n))$: general setting and the case $n=3$
• Coherent States for Quantum Compact Groups
• Heisenberg realization for U_q(sln) on the flag manifold
• Quantum Principal Bundles
• $U_q(sl(n))$ Difference Operator Realization