The inverse Serre functor of D^b_c(P^n) is the P-twist at the IC sheaf of the open stratum, and all indecomposable perverse sheaves are P-like or 0-spherical.
TQFT with corners and tilting functors in the Kac-Moody case
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
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.
fields
math.RT 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Serre functor and $\mathbb{P}$-objects for perverse sheaves on $\mathbb{P}^n$
The inverse Serre functor of D^b_c(P^n) is the P-twist at the IC sheaf of the open stratum, and all indecomposable perverse sheaves are P-like or 0-spherical.