Speaker：Naihuan Jing (North Carolina State University)

Time：2021-04-20 09:00

Location：Conference Room 105 at Experiment Building at Haiyun Campus

Abstract:

In this talk we discuss the integral form of the lattice vertex algebra $V_L$ and the associated vertex group. Dong and Griess have constructed an integral form on the vertex algebra $V_L$ spanned by Schur polynomials.We show that divided powers of general vertex operators preserve the integral lattice spanned by Schur functions indexed by partition-valued functions. We alsoshow that the generalized Garland operators, counterparts of divided powers of Heisenberg elements in affine Lie algebras, also preserve the integral form. These construe analogs of the Kostant $\mathbb Z$-forms for the enveloping algebras of simple Lie algebras and the algebraic affine Lie groups in the situation of the lattice vertex algebras.