Weight Representations of Admissible Affine Vertex Algebras

• Published in: Communications in mathematical physics Vol. 353; no. 3; pp. 1151 - 1178
• Main Authors: Arakawa, Tomoyuki, Futorny, Vyacheslav, Ramirez, Luis Enrique
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-08-2017; Springer Nature B.V
• Subjects: Algebra; Classical and Quantum Gravitation; Complex Systems; Mathematical and Computational Physics; Mathematical Physics; Modules; Physics; Physics and Astronomy; Quantum Physics; Quotients; Relativity Theory; Representations; Theoretical
• ISSN: 0010-3616; 1432-0916
• DOI: 10.1007/s00220-017-2872-3

For an admissible affine vertex algebra
V
k
(
g
)
of type
A
, we describe a new family of relaxed highest weight representations of
V
k
(
g
)
. They are simple quotients of representations of the affine Kac–Moody algebra
g
^
induced from the following
g
-modules: (1) generic Gelfand–Tsetlin modules in the principal nilpotent orbit, in particular all such modules induced from
sl
2
; (2) all Gelfand–Tsetlin modules in the principal nilpotent orbit that are induced from
sl
3
; (3) all simple Gelfand–Tsetlin modules over
sl
3
. This in particular gives the classification of all simple positive energy weight representations of
V
k
(
g
)
with finite dimensional weight spaces for
g
=
sl
3
.