Twisted modules for affine vertex algebras over fields of prime characteristic

：穆强教授
：2019-07-31 16:00
：物机大楼661

       Speaker：Prof.  Qiang Mu

                       Harbin Normal University

Title:  Twisted modules for affine vertex algebras over fields of prime characteristic

       Time：31 July 2019, 16:00

Location：物机大楼661

Abstract: In this paper, twisted modules for modular affine vertex algebras $V_{\widehat{\mathfrak{g}}}(\ell,0)$ for their quotient vertex algebras $V^{\chi}_{\widehat{\mathfrak{g}}}(\ell,0)$ with $\mathfrak{g}$ a restricted Lie algebra are studied. Let $\sigma$ be an automorphism of $\mathfrak{g}$ let $T$ be a positive integer relatively prime with the characteristic $p$ such that $\sigma^{T}=1$. It is proved that $\frac{1}{T}\mathbb{N}$-graded irreducible $\sigma$-twisted $V^{0}_{\widehat{\mathfrak{g}}}(\ell,0)$-modules are in one-to-one correspondence with irreducible modules for the restricted enveloping algebra $\mathfrak{u}(\mathfrak{g}_0)$, where $\mathfrak{g}_0$ is the subalgebra of $\sigma$-fixed points in $\mathfrak{g}$. It is also proved that when $\mathfrak{g}=\mathfrak{h}$ is abelian, the twisted Heisenberg Lie algebra $\widehat{\mathfrak{h}}[\sigma]$ is actually isomorphic to the untwisted Heisenberg Lie algebra $\widehat{\mathfrak{h}}$, unlike in the case of characteristic zero. Furthermore, for any nonzero level $\ell$, irreducible $\sigma$-twisted $L_{\widehat{\mathfrak{h}}}(\ell,0)$-modules are explicitly classified the complete reducibility of every $\sigma$-twisted $L_{\widehat{\mathfrak{h}}}(\ell,0)$-module is obtained.This is a joint work with Haisheng Li.

        联系人：谭绍滨教授