Quantum Kostka and the rank one problem for ${\mathfrak{sl}}_{2m}$

Abstract

We give necessary and sufficient conditions to specify vector bundles of conformal blocks for ${\mathfrak{sl}}_{2m}$ with rectangular weights which have ranks zero, one, and larger than one. First Chern classes of rank one bundles are shown to determine a finitely generated subcone of the nef cone.

19 pages, 12 figures

References in corpus (3)

• Conformal blocks divisors on ${\bar{M}}_{0,n}$ from $s{l}_2$
• Nonvanishing of conformal blocks divisors on ${\bar{M}}_{0,n}$
• Scaling of conformal blocks and generalized theta functions over ${\bar{M}}_{g,n}$

Cited by in corpus (1)

• Scaling of conformal blocks and generalized theta functions over ${\bar{M}}_{g,n}$