K-groups of the quantum homogeneous space SU_q(n)∕SU_q(n− 2)

Abstract

Quantum Stiefel manifolds were introduced by Vainerman and Podkolzin, who classified the irreducible representations of the C^∗-algebras underlying such manifolds. We compute the K-groups of the quantum homogeneous spaces SU_q(n)∕SU_q(n− 2) for n ≥ 3. In the case n = 3, we show that K₁ is a free ℤ-module, and the fundamental unitary for quantum SU(3) is part of a basis for K₁.