A new construction of the semi-infinite BGG resolution

Details A new construction of the semi-infinite BGG resolution A new construction of the semi-infinite BGG resolution

1996-05-29

arxiv.org/abs/q-alg/9605043v3

Mathematics

Quantum Algebra

21 pages, AMSLATEX, nonstandard page size: width 17 cm, length 24 cm

Scientific paper

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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