New developments of vertex algebra theory

(1)引入了手性微分算子的渐近代数的概念。然后，我们通过手性哈密顿约简，在慢速切片与幂零锥相交的分辨率上构造了一个这样的代数。我们计算了该代数的全局截面空间，从而证明了仿射w -代数在临界水平上的一个局部化定理。这是与T. Kuwabara和F. Malikov合作的作品。(2)引入了半无限限制函子的概念，并证明了它与仿射Kac-Moody代数可容许表示相容，从而对Kac-Wakimoto可容许表示进行了归纳研究。

(1) We have introduced the notion of an asymptotic algebra of chiral differential operators. We then have constructed, via a chiral Hamiltonian reduction, one such algebra over a resolution of the intersection of the Slodowy slice with the nilpotent cone. We compute the space of global sections of this algebra thereby proving a localization theorem for affine W-algebras at the critical level. This is a joint work with T. Kuwabara and F. Malikov.(2) We introduced a notion of semi-infinite restriction functor, and shows that it is compatible with admissibility of representations of affine Kac-Moody algebras, enabling an inductive study of Kac-Wakimoto admissible representations.