Finiteness of conformal blocks over compact Riemann surfaces

谱有限性、量子范数连续性与经典点

Spectral finiteness, quantum norm continuity and classical points

本文证明了紧量子群在希尔伯特或巴纳赫空间上的表示的统一连续性等价于谱有限性，即有限多个同型分量，并扩展了紧群在巴纳赫空间上的经典结果。

关于顶点代数共形块的分解与向量丛

On factorization and vector bundles of conformal blocks from vertex algebras

本文证明顶点算子代数表示在满足有限性和半单性条件时，其共形块层满足分解猜想并成为向量丛，为不变量递归计算及新场论构造奠定基础。

Conformal field theories associated to regular chiral vertex operator algebras I: theories over the projective line

Based on any chiral vertex operator algebra satisfying a suitable finiteness condition, the semisimplicity of the zero-mode algebra as well as a regularity for induced modules, we construct conformal field theory over the projective line with the chiral vertex operator algebra as symmetries of the theory. We appropriately generalize the argument in [TUY] so that we are able to define sheaves of conformal blocks for chiral vertex operator algebras and study them in detail. We prove the factorization theorem under the fairly general conditions for chiral vertex operator algebras and the zero-mod…