W-extended Kac representations and integrable boundary conditions in the logarithmic minimal models WLM(1, p)

Rasmussen, Jorgen (2011) W-extended Kac representations and integrable boundary conditions in the logarithmic minimal models WLM(1, p). Journal Of Physics A-Mathematical And Theoretical, 44 39 Article No.395205: 1-26. doi:10.1088/1751-8113/44/39/395205


Author Rasmussen, Jorgen
Title W-extended Kac representations and integrable boundary conditions in the logarithmic minimal models WLM(1, p)
Formatted title
W-extended Kac representations and integrable boundary conditions in the logarithmic minimal models WLM (1,p)
Journal name Journal Of Physics A-Mathematical And Theoretical   Check publisher's open access policy
ISSN 1751-8113
1751-8121
Publication date 2011-09-01
Year available 2011
Sub-type Article (original research)
DOI 10.1088/1751-8113/44/39/395205
Open Access Status Not Open Access
Volume 44
Issue 39 Article No.395205
Start page 1
End page 26
Total pages 26
Place of publication Bristol, England, U.K.
Publisher Institute of Physics Publishing
Language eng
Formatted abstract
We construct new Yang-Baxter integrable boundary conditions in the lattice approach to the logarithmic minimal model WLM(1, p) giving rise to reducible yet indecomposable representations of rank 1 in the continuum scaling limit. We interpret these W-extended Kac representations as finitely generatedW-extended Feigin-Fuchs modules over the tripletW-algebraW(p). The W-extended fusion rules of these representations are inferred from the recently conjectured Virasoro fusion rules of the Kac representations in the underlying logarithmic minimal model LM(1, p). We also introduce the modules contragredient to the W-extended Kac modules and work out the correspondingly extended fusion algebra. Our results are in accordance with the Kazhdan-Lusztig dual of tensor products of modules over the restricted quantum universal enveloping algebraU-q(sl2) at q = eπi/p. Finally, polynomial fusion rings isomorphic with the various fusion algebras are determined, and the corresponding Grothendieck ring of characters is identified.
Keyword Conformal Field-theory
Fusion algebras
Q-Index Code C1
Q-Index Status Provisional Code
Grant ID FT100100774
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Non HERDC
 
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Created: Wed, 14 Mar 2012, 20:56:49 EST by Kay Mackie on behalf of School of Mathematics & Physics