  Let g be a semisimple Lie algebra over an algebraically closed field k of
characteristic 0. Let V be a simple finite-dimensional g-module and let y\in V
be a highest weight vector. It is a classical result of B. Kostant that the
algebra of functions on the closure of the orbit of y under the simply
connected group which corresponds to g is quadratic (i.e. the closuree of the
orbit is a quadratic cone). In the present paper we extend this result of
Kostant to the case of the quantized universal enveloping algebra U_q(g). The
result uses certain information about spectrum of braiding operators for U_q(g)
due to Reshetikhin and Drinfeld.
