Semiinfinite Flags. II. Local and Global Intersection Cohomology of Quasimaps' Spaces
| dc.creator | Feigin, Boris | |
| dc.creator | Finkelberg, Michael | |
| dc.creator | Kuznetsov, Alexander | |
| dc.creator | Mirković, Ivan | |
| dc.date | 1997-11-08 | |
| dc.date | 2008-09-30 | |
| dc.date.accessioned | 2026-07-07T10:06:15Z | |
| dc.date.available | 2026-07-07T10:06:15Z | |
| dc.description | For a simple algebraic group $G$ we study the space $Q$ of Quasimaps from the projective line $C$ to the flag variety of $G$. We prove that the global Intersection Cohomology of $Q$ carries a natural pure Tate Hodge structure, and compute its generating function. We define an action of the Langlands dual Lie algebra $g^L$ on this cohomology. We present a new geometric construction of the universal enveloping algebra $U(n^L_+)$ of the nilpotent subalgebra of $g^L$. It is realized in the Ext-groups of certain perverse sheaves on Quasimaps' spaces, and it is equipped with a canonical basis numbered by the irreducible components of certain algebraic cycles, isomorphic to the intersections of semiinfinite orbits in the affine Grassmannian of $G$. We compute the stalks of the IC-sheaves on the Schubert strata closures in $Q$. They carry a natural pure Tate Hodge structure, and their generating functions are given by the generic affine Kazhdan-Lusztig polynomials. In the Appendix we prove that Kontsevich's space of stable maps provides a natural resolution of $Q$. | |
| dc.description | version published in AMS Translations | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9711009 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9711009 | |
| dc.identifier | Amer. Math. Soc. Transl. Ser. 2, vol. 194 (1999), 113--148 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170260 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Semiinfinite Flags. II. Local and Global Intersection Cohomology of Quasimaps' Spaces | |
| dc.type | text |