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

2006/05/03 by Catharina Stroppel, Stroppel, Catharina · 1 citation
Mathematics · #17B67 #57M27 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0605103

openalex publication_date 2006/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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