Basic Hypergeometric Functions and the Borel–Weil Construction for $U_q (3)$

Abstract

The Borel–Weil construction of the irreducible unitary representations of the quantum group $U_q (3)$ is investigated. The representation functions are calculated explicitly and found to be expressible in terms of basic hypergeometric functions; the form of these basis functions verifies previous general results. It is shown that several identities satisfied by basic hypergeometric functions, including a special case of Watson’s formula, are implied by properties of the quantum group.