Fusion matrices, generalized Verlinde formulas and partition functions in WLM(1, p)

Rasmussen, Jorgen (2010) Fusion matrices, generalized Verlinde formulas and partition functions in WLM(1, p). Journal of Physics A: Mathematical and Theoretical, 43 10: 105201.1-105201.28. doi:10.1088/1751-8113/43/10/105201


Author Rasmussen, Jorgen
Title Fusion matrices, generalized Verlinde formulas and partition functions in 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 2010-03
Sub-type Article (original research)
DOI 10.1088/1751-8113/43/10/105201
Volume 43
Issue 10
Start page 105201.1
End page 105201.28
Total pages 28
Place of publication Bristol, United Kingdom
Publisher Institute of Physics Publishing
Language eng
Formatted abstract
The infinite series of logarithmicminimal models LM(1, p) is considered in the
W-extended picture where they are denoted by WLM (1, p). As in the rational
models, the fusion algebra of WLM(1, p) is described by a simple graph fusion
algebra. The corresponding fusion matrices are mutually commuting, but in
general not diagonalizable. Nevertheless, they can be simultaneously brought
to Jordan form by a similarity transformation. The spectral decomposition
of the fusion matrices is completed by a set of refined similarity matrices
converting the fusion matrices into Jordan canonical form consisting of Jordan
blocks of rank 1, 2 or 3. The various similarity transformations and Jordan
forms are determined from the modular data. This gives rise to a generalized
Verlinde formula for the fusion matrices. Its relation to the partition functions
in the model is discussed in a general framework. By application of a particular
structure matrix and its Moore–Penrose inverse, this Verlinde formula reduces
to the generalized Verlinde formula for the associated Grothendieck ring.
Keyword Conformal field theories
Minimal models
Modular transformations
Graphs
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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Created: Wed, 14 Mar 2012, 11:47:12 EST by Kay Mackie on behalf of Mathematics