Singular vectors for the WN algebras

Ridout, David, Siu, Steve and Wood, Simon ORCID: https://orcid.org/0000-0002-8257-0378 2018. Singular vectors for the WN algebras. Journal of Mathematical Physics 59 (3) , 031701. 10.1063/1.5019278

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Abstract

In this paper, we use free field realisations of the A-type principal, or Casimir, WN algebras to derive explicit formulae for singular vectors in Fock modules. These singular vectors are constructed by applying screening operators to Fock module highest weight vectors. The action of the screening operators is then explicitly evaluated in terms of Jack symmetric functions and their skew analogues. The resulting formulae depend on sequences of pairs of integers that completely determine the Fock module as well as the Jack symmetric functions.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	American Institute of Physics
ISSN:	0022-2488
Funders:	Australian Research Council
Date of First Compliant Deposit:	9 March 2018
Date of Acceptance:	11 February 2018
Last Modified:	19 Nov 2024 07:15
URI:	https://orca.cardiff.ac.uk/id/eprint/109793

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