dorsal/arxiv
View SchemaLocalization of $\frak{u}$-modules. III. Tensor categories arising from configuration spaces
| Authors | M. Finkelberg, V. Schechtman |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9503013 |
| URL | https://arxiv.org/abs/q-alg/9503013 |
Abstract
This article is a sequel to hep-th/9411050, q-alg/9412017. In Chapter 1 we associate with every Cartan matrix of finite type and a non-zero complex number $\zeta$ an abelian artinian category $\FS$. We call its objects {\em finite factorizable sheaves}. They are certain infinite collections of perverse sheaves on configuration spaces, subject to a compatibility ("factorization") and finiteness conditions. In Chapter 2 the tensor structure on $\FS$ is defined using functors of nearby cycles. It makes $\FS$ a braided tensor category. In Chapter 3 we define, using vanishing cycles functors, an exact tensor functor $$\Phi:\FS\lra\CC$$ to the category $\CC$ connected with the corresponding quantum group. In Chapter 4 we show that $\Phi$ is an equivalence. Some proofs are only sketched.
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"abstract": "This article is a sequel to hep-th/9411050, q-alg/9412017.\n In Chapter 1 we associate with every Cartan matrix of finite type and a\nnon-zero complex number $\\zeta$ an abelian artinian category $\\FS$. We call its\nobjects {\\em finite factorizable sheaves}. They are certain infinite\ncollections of perverse sheaves on configuration spaces, subject to a\ncompatibility (\"factorization\") and finiteness conditions.\n In Chapter 2 the tensor structure on $\\FS$ is defined using functors of\nnearby cycles. It makes $\\FS$ a braided tensor category.\n In Chapter 3 we define, using vanishing cycles functors, an exact tensor\nfunctor $$\\Phi:\\FS\\lra\\CC$$ to the category $\\CC$ connected with the\ncorresponding quantum group.\n In Chapter 4 we show that $\\Phi$ is an equivalence. Some proofs are only\nsketched.",
"arxiv_id": "q-alg/9503013",
"authors": [
"M. Finkelberg",
"V. Schechtman"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Localization of $\\frak{u}$-modules. III. Tensor categories arising from configuration spaces",
"url": "https://arxiv.org/abs/q-alg/9503013"
},
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