INTERSECTION NUMBERS OF sl2 CONFORMAL BLOCKS COUNT POINTS IN A POLYTOPE

Abstract

“The Verlinde formula for SL2 counts the number of lattice points in a polytope.” I first heard this statement from Bernd Sturmfels in a talk at the Conference on Geometric Invariant Theory in Göttingen, June 2008. A search of the literature reveals that for sl2, this is proven in a paper of Rasmussen and Walton [6]. It is also proven for n = 3 points for sl3 in [2,7] and conjectured for slr+1 for all r ≥ 3 as well in [7]. In Section 2 we reprove this result using ideas of Boris Alexeev. In Section 3 we extend this to intersection numbers of conformal block divisors D(sl2, `, ~λ) with F-curves FI1,I2,I3,I4 . In Section 4 we describe a Sage worksheet and polymake calculation that were used to test Theorem 3.6 for n = 5 and n = 6.

Cite this paper

@inproceedings{Swinarski2012INTERSECTIONNO, title={INTERSECTION NUMBERS OF sl2 CONFORMAL BLOCKS COUNT POINTS IN A POLYTOPE}, author={David Swinarski and Bernd Sturmfels and Lauren Vogelstein}, year={2012} }