dorsal/arxiv
View SchemaFactorizable D-modules
| Authors | Sergei Khoroshkin, Vadim Schechtman |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9611018 |
| URL | https://arxiv.org/abs/q-alg/9611018 |
Abstract
A braided tensor category $FM_{\kappa}$ of `factorizable D-modules' over configuration spaces is introduced, analogous to the category $FS_q$ of factorizable sheaves from q-alg/9604001. This category is equivalent to the category of finite dimensional representations of a complex semisimple Lie algebra $\frak{g}$, with the Drinfeld's Knizhnik-Zamolodchikov tensor product. This description, together with the result of op.cit., gives a new, "Riemann-Hilbert" proof of the Drinfeld's theorem establishing an equivalence of the above tensor category with the category of finite dimensional $U_q\frak{g}$-modules ($q=\exp(2\pi i/kappa)$, $\kappa$ irrational).
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"abstract": "A braided tensor category $FM_{\\kappa}$ of `factorizable D-modules\u0027 over\nconfiguration spaces is introduced, analogous to the category $FS_q$ of\nfactorizable sheaves from q-alg/9604001. This category is equivalent to the\ncategory of finite dimensional representations of a complex semisimple Lie\nalgebra $\\frak{g}$, with the Drinfeld\u0027s Knizhnik-Zamolodchikov tensor product.\nThis description, together with the result of op.cit., gives a new,\n\"Riemann-Hilbert\" proof of the Drinfeld\u0027s theorem establishing an equivalence\nof the above tensor category with the category of finite dimensional\n$U_q\\frak{g}$-modules ($q=\\exp(2\\pi i/kappa)$, $\\kappa$ irrational).",
"arxiv_id": "q-alg/9611018",
"authors": [
"Sergei Khoroshkin",
"Vadim Schechtman"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Factorizable D-modules",
"url": "https://arxiv.org/abs/q-alg/9611018"
},
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