## Non-weight representations over the Virasoro algebra

**Speaker(s): ** Tan Haijun

**Time: ** 00:00-00:00 October 20, 2014

**Venue: ** Room 09 at Quan Zhai, BICMR

Speaker: Tan Haijun

Time: Monday, October 20, 2014 from 13:45 to 14:45

Place: Room 09 in Quan Zhai

Abstract: Let $\mathfrak{V}$ be the Virasoro algebra over the complex numbers with generators $d_i$ and $c$ (basis of the center). Let $n$ be a positive integer and let $s_n, s_{n+1}, ..., s_{2n}, \lambda, \theta$ be complex numbers such that $\lambda$ is not $0$. Let $\mathfrak{b}_{\lambda, n}$ is the subalgebra of the Virasoro algebra generated by $d_k-\lambda^{k-n+1}d_{n-1}$ for $k$ larger than or equal to $n$. There is a natural action of $\mathfrak{b}_{\lambda, n}$ on the one-dimensional vector space ${\Bbb C}$. Using this action, we obtain an induced $\mathfrak{V}$ module. We will give the necessary and sufficient conditions for this induced $\mathfrak{V}$ module to be simple. We will also generalize this construction and obtain new irreducible representations for the Virasoro algebra.

We will also introduce some non-weight representations over $\W_n$ where $W_n$ is the Lie algebra of all derivations of the Laurent polynomial algebra in $t_1$, ... $t_n$.