Relaxed singular vectors, Jack symmetric functions and fractional level slˆ(2) models
The fractional level models are (logarithmic) conformal field theories associated with affine Kac–Moody (super)algebras at certain levels k∈Q. They are particularly noteworthy because of several longstanding difficulties that have only recently been resolved. Here, Wakimoto's free field realisa...
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doaj-94980e2c56e64b81bce47f2274fa1fde2020-11-24T23:40:53ZengElsevierNuclear Physics B0550-32131873-15622015-05-01894C62166410.1016/j.nuclphysb.2015.03.023Relaxed singular vectors, Jack symmetric functions and fractional level slˆ(2) modelsDavid RidoutSimon WoodThe fractional level models are (logarithmic) conformal field theories associated with affine Kac–Moody (super)algebras at certain levels k∈Q. They are particularly noteworthy because of several longstanding difficulties that have only recently been resolved. Here, Wakimoto's free field realisation is combined with the theory of Jack symmetric functions to analyse the fractional level slˆ(2) models. The first main results are explicit formulae for the singular vectors of minimal grade in relaxed Wakimoto modules. These are closely related to the minimal grade singular vectors in relaxed (parabolic) Verma modules. Further results include an explicit presentation of Zhu's algebra and an elegant new proof of the classification of simple relaxed highest weight modules over the corresponding vertex operator algebra. These results suggest that generalisations to higher rank fractional level models are now within reach.http://www.sciencedirect.com/science/article/pii/S0550321315001054 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
David Ridout Simon Wood |
spellingShingle |
David Ridout Simon Wood Relaxed singular vectors, Jack symmetric functions and fractional level slˆ(2) models Nuclear Physics B |
author_facet |
David Ridout Simon Wood |
author_sort |
David Ridout |
title |
Relaxed singular vectors, Jack symmetric functions and fractional level slˆ(2) models |
title_short |
Relaxed singular vectors, Jack symmetric functions and fractional level slˆ(2) models |
title_full |
Relaxed singular vectors, Jack symmetric functions and fractional level slˆ(2) models |
title_fullStr |
Relaxed singular vectors, Jack symmetric functions and fractional level slˆ(2) models |
title_full_unstemmed |
Relaxed singular vectors, Jack symmetric functions and fractional level slˆ(2) models |
title_sort |
relaxed singular vectors, jack symmetric functions and fractional level slˆ(2) models |
publisher |
Elsevier |
series |
Nuclear Physics B |
issn |
0550-3213 1873-1562 |
publishDate |
2015-05-01 |
description |
The fractional level models are (logarithmic) conformal field theories associated with affine Kac–Moody (super)algebras at certain levels k∈Q. They are particularly noteworthy because of several longstanding difficulties that have only recently been resolved. Here, Wakimoto's free field realisation is combined with the theory of Jack symmetric functions to analyse the fractional level slˆ(2) models. The first main results are explicit formulae for the singular vectors of minimal grade in relaxed Wakimoto modules. These are closely related to the minimal grade singular vectors in relaxed (parabolic) Verma modules. Further results include an explicit presentation of Zhu's algebra and an elegant new proof of the classification of simple relaxed highest weight modules over the corresponding vertex operator algebra. These results suggest that generalisations to higher rank fractional level models are now within reach. |
url |
http://www.sciencedirect.com/science/article/pii/S0550321315001054 |
work_keys_str_mv |
AT davidridout relaxedsingularvectorsjacksymmetricfunctionsandfractionallevelslˆ2models AT simonwood relaxedsingularvectorsjacksymmetricfunctionsandfractionallevelslˆ2models |
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1725508807298121728 |