The Frobenius-Schur indicator in conformal field theory

Bantay, P.

doi:10.1016/s0370-2693(96)01662-0

Cited by 75 publications

(191 citation statements)

References 7 publications

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“…Suppose now that G = S 8 , the symmetric group on eight letters, and let F be cyclic of order 8. Choose a generator c of F and define an action of F on G by the requirement that the action of c be the conjugation by the 8-cycle τ := (1,2,3,4,5,6,7,8), so that c.σ = τ στ −1 . Now, if g is the 8-cycle (1, 3, 5, 8, 2, 4, 6, 7 Suppose now that Λ [4,2] were central.…”

Section: 7mentioning

confidence: 99%

On higher Frobenius-Schur indicators

Kashina¹,

Sommerhäuser²,

Zhu³

2006

Memoirs of the AMS

105

179

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Section: 7mentioning

confidence: 99%

On higher Frobenius-Schur indicators

Kashina¹,

Sommerhäuser²,

Zhu³

2006

Memoirs of the AMS

105

179

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“…As a conclusion from this In this section we will derive explicit Frobenius-Schur (FS)-indicator formulae for two kinds of quasi-Hopf algebras associated to a 3-cocycle on a finite group G. In particular, Bantay's formula for the second FS-indicator for a twisted quantum double of a finite group derived in [MN05] is a special case of these formulae (see also [Ban00] and [Ban97]). …”

Section: Examples and Applicationsmentioning

confidence: 99%

Central invariants and higher indicators for semisimple quasi-Hopf algebras

Schauenburg

2007

Trans. Amer. Math. Soc.

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Abstract. In this paper, we define the higher Frobenius-Schur (FS-)indicators for finite-dimensional modules of a semisimple quasi-Hopf algebra H via the categorical counterpart developed in a 2005 preprint. When H is an ordinary Hopf algebra, we show that our definition coincides with that introduced by Kashina, Sommerhäuser, and Zhu. We find a sequence of gauge invariant central elements of H such that the higher FS-indicators of a module V are obtained by applying its character to these elements. As an application, we show that FS-indicators are sufficient to distinguish the four gauge equivalence classes of semisimple quasi-Hopf algebras of dimension eight corresponding to the four fusion categories with certain fusion rules classified by Tambara and Yamagami. Three of these categories correspond to well-known Hopf algebras, and we explicitly construct a quasi-Hopf algebra corresponding to the fourth one using the Kac algebra. We also derive explicit formulae for FS-indicators for some quasi-Hopf algebras associated to group cocycles.

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“…One may expect the symmetry Ω to be closely related to the choice of Klein bottle projection K i , which determines the projection in the closed string sector. The link between the two is provided by a relation postulated in [18]: 24) conjectured to hold without summation on j. Here we restored the dependence on g, that was absorbed into the definition of B in [18].…”

Section: This Leads To the Following Expressionmentioning

confidence: 73%

“…⋆ Note that Y j 00 is equal to the Frobenius-Schur indicator [24][20], which vanishes for complex fields.…”

Section: This Leads To the Following Expressionmentioning

confidence: 99%

Orientation matters for NIMreps

Sousa¹,

Schellekens²

2003

Nuclear Physics B

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The problem of finding boundary states in CFT, often rephrased in terms of "NIMreps" of the fusion algebra, has a natural extension to CFT on non-orientable surfaces.This provides extra information that turns out to be quite useful to give the proper interpretation to a NIMrep. We illustrate this with several examples. This includes a rather detailed discussion of the interesting case of the simple current extension of A 2 level 9, which is already known to have a rich structure. This structure can be disentangled completely using orientation information. In particular we find here and in other cases examples of diagonal modular invariants that do not admit a NIMrep, suggesting that there does not exist a corresponding CFT. We obtain the complete set of NIMreps (plus Moebius and Klein bottle coefficients) for many exceptional modular invariants of WZW models, and find an explanation for the occurrence of more than one NIMrep in certain cases. We also (re)consider the underlying formalism, emphasizing the distinction between oriented and unoriented string annulus amplitudes, and the origin of orientation-dependent degeneracy matrices in the latter.

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The Frobenius-Schur indicator in conformal field theory

Abstract: : An analogue of the classical Frobenius-Schur indicator is introduced in order to distinguish between real and pseudo-real self-conjugate primary fields, and an explicit expression for this quantity is derived from the trace of the braiding operator.

Cited by 75 publications

References 7 publications

On higher Frobenius-Schur indicators

On higher Frobenius-Schur indicators

Central invariants and higher indicators for semisimple quasi-Hopf algebras

Orientation matters for NIMreps

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