uVertex algebras and representation theory
for full toroidal Lie algebrasv
utFYuly Billig
iJ[gεwE³φj
ϊF½¬PVNVPTϊ(ΰ)@PUFOO`PVFOO
κF©RnwncWPS
Abstract
We introduce a category of bounded modules for the full toroidal
Lie algebras. Using the fact that the full toroidal algebras are vertex
Lie algebras, we construct the toroidal vertex operator algebra. This VOA
controls the representation theory of toroidal Lie algebras, and every
irreducible module in the category of bounded modules is a simple module
for the toroidal VOA. This allows us to give explicit realizations for
the irreducible bounded modules and find their characters.
γͺμΜz[y[WΦ
