Regular representations of vertex operator algebras, I
| dc.creator | Li, Haisheng | |
| dc.date | 1999-08-19 | |
| dc.date.accessioned | 2026-07-07T05:30:25Z | |
| dc.date.available | 2026-07-07T05:30:25Z | |
| dc.description | In this paper, given a module $W$ for a vertex operator algebra $V$ and a nonzero complex number $z$ we construct a canonical (weak) $V\otimes V$-module ${\cal{D}}_{P(z)}(W)$ (a subspace of $W^{*}$ depending on $z$). We prove that for $V$-modules $W, W_{1}$ and $W_{2}$, a $P(z)$-intertwining map of type ${W'\choose W_{1}W_{2}}$ ([H3], [HL0-3]) exactly amounts to a $V\otimes V$-homomorphism from $W_{1}\otimes W_{2}$ into ${\cal{D}}_{P(z)}(W)$. Using Huang and Lepowsky's one-to-one linear correspondence between the space of intertwining operators and the space of $P(z)$-intertwining maps of the same type we obtain a canonical linear isomorphism from the space ${\cal{V}}^{W'}_{W_{1}W_{2}}$ of intertwining operators of the indicated type to $\Hom_{V\otimes V}(W_{1}\otimes W_{2},{\cal{D}}_{P(z)}(W))$. In the case that $W=V$, we obtain a decomposition of Peter-Weyl type for ${\cal{D}}_{P(z)}(V)$, which are what we call the regular representations of $V$. | |
| dc.description | 42 pages, latex | |
| dc.identifier | https://arxiv.org/abs/math/9908108 | |
| dc.identifier | http://arxiv.org/abs/math/9908108 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78985 | |
| dc.subject | Quantum Algebra | |
| dc.title | Regular representations of vertex operator algebras, I | |
| dc.type | text |