  Schubert varieties in the full flag variety of Kac-Moody type are indexed by
elements of the corresponding Weyl group. We give a practical criterion for
when two such Schubert varieties (from potentially different flag varieties)
are isomorphic, in terms of the Cartan matrix and reduced words for the
indexing Weyl group elements. As a corollary, we show that two such Schubert
varieties are isomorphic if and only if there is an isomorphism between their
integral cohomology rings that preserves the Schubert basis.
