Conformal blocks for quasi-lisse vertex algebras

Abstract: The space of conformal blocks is an important construct through which representation theory of infinite dimensional algebras and the geometry of complex curves influence one another. A celebrated theorem of Y. Zhu, for example, uses conformal blocks of a rational vertex algebra localised over an elliptic curve to prove modularity of its characters. We study the conformal blocks of vertex algebras localised over elliptic curves plus holomorphic line bundle. We prove that, for vertex algebras satisfying a condition we call ``stable rationality'', characters are flat sections of a modular-invariant holonomic D-module over the moduli space. Joint work with Tomoyuki Arakawa and Hao Li.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar