ar X iv : a lg - g eo m / 9 71 10 09 v 1 8 N ov 1 99 7 SEMIINFINITE FLAGS . II . LOCAL AND GLOBAL INTERSECTION COHOMOLOGY OF QUASIMAPS ’ SPACES

One of the main results of the present work is a computation of local IC stalks of the Schubert strata closures in the spaces Z. We prove that the generating functions of these stalks are given by the generic (or periodic) Kazhdan-Lusztig polynomials, see the Theorem 6.9. We understand that this result was known to G.Lusztig for a long time, cf. [L3] §11. His proof was never published though, and as far as we understand, it differs from ours: for example we never managed to find a direct geometric proof of the key property [L1] 11.1.(iv) of Lusztig’s R-polynomials.