TQFT with corners and tilting functors in the Kac-Moody case

Details TQFT with corners and tilting functors in the Kac-Moody case TQFT with corners and tilting functors in the Kac-Moody case

2006-05-03

arxiv.org/abs/math/0605103v1

Mathematics

Representation Theory

Scientific paper

We study projective functors (i.e. direct summands of compositions of translations through walls) for parabolic versions of $\cO$ as well as for integral regular blocks outside the critical hyperplanes in the symmetrizable Kac-Moody case. It turns out that in both situations the functors are completely determined by their restriction to the additive category generated by (the limit of) a `full projective tilting' object. We describe how projective functors in the parabolic setup give rise to an invariant of tangle cobordisms and formulate a conjectural direct connection to Khovanov homology. Our main result, however, is the classification theorem for indecomposable projective functors in the Kac-Moody case verifying a conjecture of F. Malikov and I. Frenkel.

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