On charged fields with group symmetry and degeneracies of Verlinde’s matrix S *
Annales de l'I.H.P. Physique théorique, Volume 71 (1999) no. 4, pp. 359-394.
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     author = {M\"uger, Michael},
     title = {On charged fields with group symmetry and degeneracies of {Verlinde{\textquoteright}s} matrix $S^\ast $},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {359--394},
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     url = {http://www.numdam.org/item/AIHPA_1999__71_4_359_0/}
}
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Müger, Michael. On charged fields with group symmetry and degeneracies of Verlinde’s matrix $S^\ast $. Annales de l'I.H.P. Physique théorique, Volume 71 (1999) no. 4, pp. 359-394. http://www.numdam.org/item/AIHPA_1999__71_4_359_0/

[1] C. D'Antoni and R. Longo, Interpolation by type I factors and the flip automorphism, J. Funct. Anal. 51 (1983) 361-371. | MR | Zbl

[2] C. D'Antoni, Technical properties of the quasilocal algebra, in: D. Kastler, ed., The Algebraic Theory of Superselection Sectors. Introduction and Recent Results, World Scientific, 1990.

[3] J. Böckenhauer and D.E. Evans, Modular invariants, graphs and α-induction for nets of subfactors I, Commun. Math. Phys. 197 (1998) 361-386. | MR | Zbl

[4] R. Brunetti, D. Guido and R. Longo, Modular structure and duality in QFT, Commun. Math. Phys. 156 (1993) 201-219. | MR | Zbl

[5] D. Buchholz, G. Mack and I. Todorov, The current algebra on the circle as a germ of local field theories, Nucl. Phys. B (Proc. Suppl.) 5B (1988) 20-56. | MR | Zbl

[6] D. Buchholz, S. Doplicher and R. Longo, On Noether's theorem in quantum field theory, Ann. Phys. 170 (1986) 1-17. | MR | Zbl

[7] D. Buchholz, S. Doplicher, R. Longo and J. Roberts, Extensions of automorphisms and gauge symmetries, Commun. Math. Phys. 155 (1993) 123- 134. | MR | Zbl

[8] R. Conti, unpublished.

[9] R. Dijkgraaf, C. Vafa, E. Verlinde and H. Verlinde, The operator algebra of orbifold models, Commun. Math. Phys. 123 (1989) 485-527. | MR | Zbl

[10] S. Doplicher, R. Haag and J.E. Roberts, Fields, observables and gauge transformations I, Commun. Math. Phys. 13 (1969) 1-23. | MR | Zbl

[11] S. Doplicher, R. Haag and J.E. Roberts, Fields, observables and gauge transformations II, Commun. Math. Phys. 15 (1969) 173-200. | MR | Zbl

[12] S. Doplicher, R. Haag and J.E. Roberts, Local observables and particle statistics I, Commun. Math. Phys. 23 (1971) 199-230. | MR

[13] S. Doplicher and J.E. Roberts, Fields, statistics and non-abelian gauge groups, Commun. Math. Phys. 28 (1972) 331-348. | MR

[14] S. Doplicher, R. Haag and J.E. Roberts, Local observables and particle statistics II, Commun. Math. Phys. 35 (1974) 49-85. | MR

[15] S. Doplicher, Local aspects of superselection rules, Commun. Math. Phys. 85 (1982) 73-86. | MR | Zbl

[16] S. Doplicher and R. Longo, Standard and split inclusions of von Neumann algebras, Invent. Math. 75 (1984) 493-536. | MR | Zbl

[17] S. Doplicher and J.E. Roberts, A remark on compact automorphism groups of C*-algebras, J. Funct. Anal. 66 (1986) 67-72. | MR | Zbl

[18] S. Doplicher and J.E. Roberts, Duals of compact Lie groups realized in the Cuntz algebras and their actions on C*-algebras, J. Funct. Anal. 74 (1987) 96- 120. | MR | Zbl

[19] S. Doplicher and J.E. Roberts, Compact group actions on C*-algebras, J. Oper. Theor. 19 (1988) 283-305. | MR | Zbl

[20] S. Doplicher and J.E. Roberts, Endomorphisms of C*-algebras, cross products and duality for compact groups, Ann. Math. 130 (1989) 75-119. | MR | Zbl

[21] S. Doplicher and J.E. Roberts, A new duality theory for compact groups, Invent. Math. 98 (1989) 157-218. | MR | Zbl

[22] S. Doplicher and J.E. Roberts, Why there is a field algebra with a compact gauge group describing the superselection structure in particle physics, Commun. Math. Phys. 131 (1990) 51-107. | MR | Zbl

[23] K. Fredenhagen, K.-H. Rehren and B. Schroer, Superselection sectors with braid group statistics and exchange algebras I, General theory, Commun. Math. Phys. 125 (1989) 201-226. | MR | Zbl

[24] K. Fredenhagen, K.-H. Rehren and B. Schroer, Superselection sectors with braid group statistics and exchange algebras II. Geometric aspects and conformal covariance, Rev. Math. Phys. (Special Issue) (1992) 113-157. | MR | Zbl

[25] J. Fuchs, A.N. Schellekens and C. Schweigert, A matrix S for all simple current extensions, Nucl. Phys. B 473 (1996) 323-366. | MR | Zbl

[26] F. Gabbiani and J. Fröhlich, Operator algebras and conformal field theory, Commun. Math. Phys. 155 (1993) 569-640. | MR | Zbl

[27] D. Guido and R. Longo, The conformal spin-statistics theorem, Commun. Math. Phys. 181 (1996) 11-35. | MR | Zbl

[28] R. Haag, Local Quantum Physics, 2nd Ed., Springer, 1996. | MR | Zbl

[29] E. Hewitt and K.A. Ross, Abstract Harmonic Analysis I, 2nd Ed., Springer, 1979. | MR

[30] D. Kastler (ed.), The Algebraic Theory of Superselection Sectors. Introduction and Recent Results, World Scientific, 1990. | MR

[31] R. Longo, Simple injective subfactors, Adv. Math. 63 (1987) 152-171. | MR | Zbl

[32] R. Longo, Index of subfactors and statistics of quantum fields I, Commun. Math. Phys. 126 (1989) 217-247. | MR | Zbl

[33] R. Longo and K.-H. Rehren, Nets of subfactors, Rev. Math. Phys. 7 (1995) 567- 597. | MR | Zbl

[34] R. Longo and J.E. Roberts, A theory of dimension, K-Theory 11 (1997) 103- 159. | MR | Zbl

[35] M. Lüscher and G. Mack, Global conformal invariance in QFT, Commun. Math. Phys. 41 (1975) 203-234. | MR

[36] M. Müger, Quantum double actions on operator algebras and orbifold quantum field theories, Commun. Math. Phys. 191 (1998) 137-181. | MR | Zbl

[37] M. Müger, Superselection structure of massive quantum field theories in 1 + 1 dimensions, Rev. Math. Phys. 10 (1998) 1147-1170. | MR | Zbl

[38] M. Müger, On the algebraic structure of rational conformal theories, in preparation.

[39] K.-H. Rehren, Braid group statistics and their superselection rules, in: D. Kastler, ed., The Algebraic Theory of Superselection Sectors. Introduction and Recent Results, World Scientific, 1990. | MR

[40] K.-H. Rehren, Markov traces as characters for local algebras, Nucl. Phys. B (Proc. Suppl.) 18B (1990) 259-268. | MR | Zbl

[41] J.E. Roberts, Cross products of von Neumann algebras by group duals, Sympos. Math. 20 (1976) 335-363. | MR | Zbl

[42] J.E. Roberts, Local cohomology and superselection structure, Commun. Math. Phys. 51 (1976) 107-119. | MR | Zbl

[43] J.E. Roberts, Net cohomology and its applications to field theory, in: L. Streit, ed., Quantum Fields, Particles, Processes, Springer, 1980. | MR | Zbl

[44] J.E. Roberts, Lectures on algebraic quantum field theory, in: D. Kastler, ed., The Algebraic Theory of Superselection Sectors. Introduction and Recent Results, World Scientific, 1990. | MR

[45] A.N. Schellekens and S. Yankielowicz, Simple currents, modular invariants, and fixed points, Int. J. Mod. Phys. A 5 (1990) 2903-2952. | MR | Zbl

[46] S.J. Summers, Normal product states for Fermions and twisted duality for CCR- and CAR-type algebras with application to the Yukawa2 quantum field model, Commun. Math. Phys. 86 (1982) 111-141. | MR | Zbl

[47] E. Verlinde, Fusion rules and modular transformations in 2D conformal field theory, Nucl. Phys. B 300 (1988) 360-376. | MR