K-THEORY OF TWISTED DIFFERENTIAL-OPERATORS ON FLAG VARIETIES

Let g be a semisimpIe Lie algebra over k, an algebraically closed fiel d of characteristic zero, and let h subset of b be a Cartan subalgebra inside a Borel subalgebra of g. Let U be the enveloping algebra of g. For mu is an element of h let M(mu) denote the corresponding Verma m odule and let U-mu = U/Ann M(mu). Let W be the Weyl group and let W-mu (0) be the stabiliser of mu in W. We prove the following theorem, whic h affirms a conjecture of T.J. Hodges.