NDLI: Zero Modes’ Fusion Ring and Braid Group Representations for the Extended Chiral su(2) WZNW Model

Content Provider	Springer Nature Link
Author	Hadjiivav, Ludmil Todorov, Ivan Furlan, Paolo
Copyright Year	2007
Abstract	A zero modes’ Fock space $$\mathcal{F}_{q}$$ is constructed for the extended chiral $${su(2)}$$ WZNW model. It gives room to a realization of the fusion ring of representations of the restricted quantum universal enveloping algebra $$\bar{U}_{q}=\bar{U}_{q} sl(2)$$ at an even root of unity, $$q^h=-1,$$ and of its infinite dimensional extension $$\tilde{U}_{q}$$ by the Lusztig operators $$E^{(h)}, F^{(h)}.$$ We provide a streamlined derivation of the characteristic equation for the Casimir invariant from the defining relations of $$\bar{U}_{q}.$$ A central result is the characterization of the Grothendieck ring of both $$\bar{U}_{q}$$ and $$\tilde{U}_{q}$$ in Theorem 3.1. The properties of the $$\tilde{U}_{q}$$ fusion ring in $$\mathcal{F}_{q}$$ are related to the braiding properties of correlation functions of primary fields of the conformal $$\widehat{su}(2)_{h-2}$$ current algebra model.
Ending Page	151
Page Count	35
Starting Page	117
File Format	PDF
ISSN	03779017
e-ISSN	15730530
Journal	Letters in Mathematical Physics
Issue Number	2-3
Volume Number	82
Language	English
Publisher	Springer Netherlands
Publisher Date	2007-12-05
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Geometry fusion ring Mathematical and Computational Physics factorizable Hopf algebra Quantum groups (quantized enveloping algebras) and related deformations Constructive quantum field theory Group Theory and Generalizations Grothendieck groups, $K$-theory Extended chiral WZNW model braid group Statistical Physics indecomposable representations
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Mathematical Physics

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