dorsal/arxiv
View SchemaLocalization of $\frak{u}$-modules. IV. Localization on $\Bbb{P}^1$
| Authors | M. Finkelberg, V. Schechtman |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9506011 |
| URL | https://arxiv.org/abs/q-alg/9506011 |
Abstract
This article is a sequel to hep-th/9411050, q-alg/9412017, q-alg/9503013. Given a collection of $m$ finite factorizable sheaves $\{\CX_k\}$, we construct here some perverse sheaves over configuration spaces of points on a projective line $\BP^1$ with $m$ additional marked points. We announce here (with sketch proof) the computation of the cohomology spaces of these sheaves. They turn out to coincide with certain "semiinfinite" $\Tor$ spaces of the corresponding $\fu$-modules. As a corollary, we get a description of local systems of conformal blocks in WZW models in genus $0$ (cf. ~\cite{ms}) as natural subquotients of some semisimple local systems of geometric origin. In particular, these local systems are semisimple themselves.
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"date_created": "2026-03-02T18:01:24.709000Z",
"date_modified": "2026-03-02T18:01:24.709000Z",
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"abstract": "This article is a sequel to hep-th/9411050, q-alg/9412017, q-alg/9503013.\nGiven a collection of $m$ finite factorizable sheaves $\\{\\CX_k\\}$, we construct\nhere some perverse sheaves over configuration spaces of points on a projective\nline $\\BP^1$ with $m$ additional marked points. We announce here (with sketch\nproof) the computation of the cohomology spaces of these sheaves. They turn out\nto coincide with certain \"semiinfinite\" $\\Tor$ spaces of the corresponding\n$\\fu$-modules. As a corollary, we get a description of local systems of\nconformal blocks in WZW models in genus $0$ (cf. ~\\cite{ms}) as natural\nsubquotients of some semisimple local systems of geometric origin. In\nparticular, these local systems are semisimple themselves.",
"arxiv_id": "q-alg/9506011",
"authors": [
"M. Finkelberg",
"V. Schechtman"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Localization of $\\frak{u}$-modules. IV. Localization on $\\Bbb{P}^1$",
"url": "https://arxiv.org/abs/q-alg/9506011"
},
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"source": {
"execution_id": "c609ca23-a792-4b8f-b063-751d4663a46b",
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"variant": "snapshot-2026-03-01",
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