Pure and Applied Mathematics Quarterly

Volume 11 (2015)

Number 2

Quasi-minuscule $E_n$ bundles and level-one $\widehat{E}_n$ bundles over rational surfaces and VOA structures

Pages: 221 – 237

DOI: http://dx.doi.org/10.4310/PAMQ.2015.v11.n2.a2

Author

Yunxia Chen (School of Science, East China University of Science and Technology, Shanghai, China)

Abstract

In this paper, we consider a surface with only singularities of type $A$ whose smoothing is a $\mathbb{P}^2$ blown up at $8$ (resp. $9$) points. we use lines on such smooth surface to construct all the quasi-minuscule (resp. level one fundamental) representation bundles of $E_n$ (resp. affine $E_n$) over them. We also consider the vertex operator algebra structures on these bundles.

Keywords

quasi-minuscule representation bundles, level-one fundamental representation bundles

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