Universal KZB equations I: the elliptic case

Details Universal KZB equations I: the elliptic case Universal KZB equations I: the elliptic case

2007-02-22

arxiv.org/abs/math/0702670v2

Algebra, arithmetic, and geometry: in honor of Yu. I. Manin. Vol. I, 165--266, Progr. Math., 269, Birkh\"auser Boston, Inc., B

Mathematics

Quantum Algebra

Correction of reference of Thm. 9.12 stating an equivalence of categories between modules over the rational Cherednik algebra

Scientific paper

We define a universal version of the Knizhnik-Zamolodchikov-Bernard (KZB) connection in genus 1. This is a flat connection over a principal bundle on the moduli space of elliptic curves with marked points. It restricts to a flat connection on configuration spaces of points on elliptic curves, which can be used for proving the formality of the pure braid groups on genus 1 surfaces. We study the monodromy of this connection and show that it gives rise to a relation between the KZ associator and a generating series for iterated integrals of Eisenstein forms. We show that the universal KZB connection realizes as the usual KZB connection for simple Lie algebras, and that in the sl_n case this realization factors through the Cherednik algebras. This leads us to define a functor from the category of equivariant D-modules on sl_n to that of modules over the Cherednik algebra, and to compute the character of irreducible equivariant D-modules over sl_n which are supported on the nilpotent cone.

Affiliated with

Also associated with

No associations

Rating

Universal KZB equations I: the elliptic case does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Universal KZB equations I: the elliptic case, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Universal KZB equations I: the elliptic case will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-102333