dorsal/arxiv
View SchemaA new construction of the semi-infinite BGG resolution
| Authors | Sergey Arkhipov |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9605043 |
| URL | https://arxiv.org/abs/q-alg/9605043 |
Abstract
We introduce the techniques of semiregular bimodules over a Lie algebra with respect to a Lie subalgebra. Using this techniques in the case of affine Lie algebras we introduce twisting functors on the categories of modules. These functors are enumerated by elements of the affine Weyl group corresponding to the chosen affine Lie algebra and map Verma modules to so called twisted Verma modules. Applying twisting functors to the BGG resolution of an integrable simple module we obtain a sequence of complexes called the twisted BGG resolutions. We show that the twisted BGG resolutions form an inductive system of complexes. It turns out that the limit complex of the inductive system is exactly the semi-infinite BGG resolution introduced by B. Feigin and E. Frenkel and consisting of direct sums of Wakimoto modules.
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"abstract": "We introduce the techniques of semiregular bimodules over a Lie algebra with\nrespect to a Lie subalgebra. Using this techniques in the case of affine Lie\nalgebras we introduce twisting functors on the categories of modules. These\nfunctors are enumerated by elements of the affine Weyl group corresponding to\nthe chosen affine Lie algebra and map Verma modules to so called twisted Verma\nmodules. Applying twisting functors to the BGG resolution of an integrable\nsimple module we obtain a sequence of complexes called the twisted BGG\nresolutions. We show that the twisted BGG resolutions form an inductive system\nof complexes. It turns out that the limit complex of the inductive system is\nexactly the semi-infinite BGG resolution introduced by B. Feigin and E. Frenkel\nand consisting of direct sums of Wakimoto modules.",
"arxiv_id": "q-alg/9605043",
"authors": [
"Sergey Arkhipov"
],
"categories": [
"q-alg",
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"title": "A new construction of the semi-infinite BGG resolution",
"url": "https://arxiv.org/abs/q-alg/9605043"
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