Erratum to: Quiver varieties and Demazure modules

Abstract

Part of the proofs of Proposition 6.1 and Theorem 8.1 relied on the statement that if w = ril · · · ri1 is a reduced expression of an element of theWeyl group and X ∈ Bw(d), then X = ẽ1 i1 · · · ẽ nl il Xw for some n1, . . . , nl ∈ Z≥0. In fact, this is not true. A counterexample can be found in [1, Example 4.6.3]. However, Propositions 6.1 and 8.1 still hold. Arguments avoiding the above claim are presented below.We thankH. Nakajima and S. Naito for bringing the error to our attention.