The Algebra of SL3(ℂ) Conformal Blocks

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11 Scopus citations


We construct and study a family of toric degenerations of the Cox ring of the moduli of quasi-parabolic principal SL3(ℂ) bundles on a smooth, marked curve (C, p→): Elements of this algebra have a well known interpretation as conformal blocks, from the Wess-Zumino-Witten model of conformal field theory. For the genus 0; 1 cases we find the level of conformal blocks necessary to generate the algebra. In the genus 0 case we also find bounds on the degrees of relations required to present the algebra. As a consequence we obtain a toric degeneration for the projective coordinate ring of an effective divisor on the moduli MC,p→(SL3(ℂ)) of quasi-parabolic principal SL3(ℂ) bundles on (C, p→). Along the way we recover positive polyhedral rules for counting conformal blocks.

Original languageEnglish
Pages (from-to)1165-1187
Number of pages23
JournalTransformation Groups
Issue number4
StatePublished - Dec 2013

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology


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