Representation theory of the vertex algebra $W_{1 + \infty}$
| dc.creator | Kac, Victor | |
| dc.creator | Radul, Andrey | |
| dc.date | 1995-12-18 | |
| dc.date.accessioned | 2026-07-07T04:21:45Z | |
| dc.date.available | 2026-07-07T04:21:45Z | |
| dc.description | In our paper~\cite{KR} we began a systematic study of representations of the universal central extension $\widehat{\Cal D}\/$ of the Lie algebra of differential operators on the circle. This study was continued in the paper~\cite{FKRW} in the framework of vertex algebra theory. It was shown that the associated to $\widehat {\Cal D}\/$ simple vertex algebra $W_{1+ \infty, N}\/$ with positive integral central charge $N\/$ is isomorphic to the classical vertex algebra $W (gl_N)$, which led to a classification of modules over $W_{1 + \infty, N}$. In the present paper we study the remaining non-trivial case, that of a negative central charge $-N$. The basic tool is the decomposition of $N\/$ pairs of free charged bosons with respect to $gl_N\/$ and the commuting with $gl_N\/$ Lie algebra of infinite matrices $\widehat{gl}$. | |
| dc.description | 26 pages, AMS-TeX, all macros included | |
| dc.identifier | https://arxiv.org/abs/hep-th/9512150 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9512150 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/54451 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Representation theory of the vertex algebra $W_{1 + \infty}$ | |
| dc.type | text |