Fusion of irreducible modules in WLM(p,p')

Rasmussen, Jorgen (2010) Fusion of irreducible modules in WLM(p,p'). Journal of Physics A: Mathematical and Theoretical, 43 4: 045210.1-045210.27. doi:10.1088/1751-8113/43/4/045210


Author Rasmussen, Jorgen
Title Fusion of irreducible modules in WLM(p,p')
Formatted title
Fusion of irreducible modules in WLM(p,p')
Journal name Journal of Physics A: Mathematical and Theoretical   Check publisher's open access policy
ISSN 1751-8113
1751-8121
Publication date 2010-01-29
Sub-type Article (original research)
DOI 10.1088/1751-8113/43/4/045210
Volume 43
Issue 4
Start page 045210.1
End page 045210.27
Total pages 27
Place of publication Bristol, United Kingdom
Publisher Institute of Physics Publishing
Language eng
Formatted abstract
Based on symmetry principles, we derive a fusion algebra generated from repeated fusions of the irreducible modules appearing in the W-extended logarithmic minimal model WLM(p, p'). In addition to the irreducible modules themselves, closure of the commutative and associative fusion algebra requires the participation of a variety of reducible yet indecomposable modules. We conjecture that this fusion algebra is the same as the one obtained by application of the Nahm-Gaberdiel-Kausch algorithm and find that it reproduces the known such results for WLM( 1, p') and WLM(2, 3). For p > 1, this fusion algebra does not contain a unit. Requiring that the spectrum of modules is invariant under a natural notion of conjugation, however, introduces additional (p - 1)(p' - 1) reducible yet indecomposable rank-1 modules, among which the identity is found, still yielding a well-defined fusion algebra. In this greater fusion algebra, the aforementioned symmetries are generated by fusions with the three irreducible modules of conformal weights Δkp-1,1, k = 1, 2, 3. We also identify polynomial fusion rings associated with our fusion algebras.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ
Additional Notes Article # 045210

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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Created: Wed, 14 Mar 2012, 12:22:41 EST by Kay Mackie on behalf of School of Mathematics & Physics