  We introduce new notions in elliptic Schubert calculus: the (twisted)
Borisov-Libgober classes of Schubert varieties in general homogeneous spaces
G/P. While these classes do not depend on any choice, they depend on a set of
new variables. For the definition of our classes we calculate multiplicities of
some divisors in Schubert varieties, which were only known for full flag
varieties before. Our approach leads to a simple recursions for the elliptic
classes. Comparing this recursion with R-matrix recursions of the so-called
elliptic weight functions of Rimanyi-Tarasov-Varchenko we prove that weight
functions represent elliptic classes of Schubert varieties.
