The Algebra of Conformal Blocks

Details The Algebra of Conformal Blocks The Algebra of Conformal Blocks

2009-10-03

arxiv.org/abs/0910.0577v5

Mathematics

Algebraic Geometry

14 figures

Scientific paper

We construct a flat sheaf of algebras over the moduli stack of stable punctured curves with fiber over a given curve equal to the Cox ring of the moduli of quasiparabolic principal bundles associated to a simple complex reductive group, also known as the algebra of conformal blocks. This construction generalizes the connection between the Hilbert functions from phylogenetic algebraic geometry and the Verlinde formula, as recently discovered by Sturmfels and Xu, gives phylogenetic varieties as Gorenstein toric deformations of the universal torsor of the moduli of quasiparabolic $SL_2(\C)$ principle bundles bundles over a curve, and answers a conjecture of Millson. We also study the relationship between these algebras and classical branching algebras of the associated simply connected reductive group in the general case, and speculate on a recipe for toric deformations of moduli of semistable quasiparabolic principal bundles for more general groups.

Affiliated with

Also associated with

No associations

Rating

The Algebra of Conformal Blocks 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 The Algebra of Conformal Blocks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Algebra of Conformal Blocks will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-664928