Localization of $\frak{u}$-modules. II. Configuration spaces and quantum groups
| dc.creator | Finkelberg, M. | |
| dc.creator | Schechtman, V. | |
| dc.date | 1995-01-01 | |
| dc.date | 1995-01-22 | |
| dc.date.accessioned | 2026-07-07T09:04:49Z | |
| dc.date.available | 2026-07-07T09:04:49Z | |
| dc.description | This paper is a sequel to "Localization of $\frak{u}$-modules. I", hep-th/9411050. We are starting here the geometric study of the tensor category $\cal{C}$ associated with a quantum group (corresponding to a Cartan matrix of finite type) at a root of unity. The main results establish isomorphisms between homogeneous components of irreducible objects in $\cal{C}$ and spaces of vanishing cycles at the origin of certain Goresky-MacPherson sheaves on configuration spaces; establish isomorphisms of the stalks at the origin of the above GM sheaves with certain Hochschild complexes (which compute the Hochschild homology of a certain "triangular" subalgebra of our quantum group with coefficients in the coresponding irreducible representation); establish the analogous results for tensor products of irreducibles. In geometry, the tensor product of representations corresponds to a "fusion" of sheaves on configuration spaces --- operation defined using the functor of nearby cycles. | |
| dc.description | 59 pages, amslatex. A number of corrections made; an error in sec. 12 corrected. We recommend this version for those who want to get a more technical acquaintance with the article | |
| dc.identifier | https://arxiv.org/abs/q-alg/9412017 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9412017 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149518 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.title | Localization of $\frak{u}$-modules. II. Configuration spaces and quantum groups | |
| dc.type | text |