Preview
Unable to display preview. Download preview PDF.
References
V. Bargmann and I.T. Todorov, Spaces of analytic functions on a complex cone as carries for the symmetric tensor representations of SO(n), J. Math. Phys. 18 (1977) 1141–1148.
A.A. Belavin, A.M. Polyakov and A.B. Zamolodchikov, Infinite conformal symmetry in two-dimensional quantum field theory, Nucl. Phys. B365 (1991) 98–120.
N. N. Bogolubov, A.A. Logunov, A.I. Oksak and I.T. Todorov, General Principles of Quantum Field Theory, Kluwer Academic Publ., Dordrecht (1990).
A. Cappelli, C. Itzykson and J. B. Zuber, The A-D-E classification of minimal and A (1)1 conformal invariant theories, Commun. Math. Phys. 113 (1987) 1–26.
P. Christie and R. Flume, The four point correlations of all primary fields of the d=2 conformally invariant SU(2) σ-model with a Wess-Zumino term, Nucl. Phys., B282 (1987) 466–494
A. Coste and T. Gannon, Galois symmetry in RCFT, Phys. Lett. B323 (1994) 316–321.
Vl.S. Dotsenko, V.A. Fateev, Conformal algebra and multipoint correlation functions in 2D statistical models, Nucl Phys. B240 (1984) 312–348.
S. Doplicher, 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 (1991) 51–107.
V.G. Drinfeld, Hopf algebras and the quantum Yang-Baxter equation, Soviet Math. Dokl. 32 (1985) 254–258.
V.G. Drinfeld, Quantum groups, in Proc. 1986 I.C.M., Amer. Math. Soc. Berkeley, CA 1 (1987) 798–820
V.G. Drinfield, Quasihopf algebras and Knizhnik-Zamolodchikov equations, Alg. i Anal. 1:6 (1989) 114–148; English transl.: Leningrad Math. J. 1 (1990), 1419–1457.
F. Falceto, K. Gawedzki, Lattice Wess-Zumino-Witten model and quantum groups, J. Geom. Phys. 11 (1993) 251–279.
L.D. Faddeev, N.Yu. Reshetikhin and L.A. Takhtajan, Quantization of Lie groups and Lie algebras, (English transl. Leningrad Math. J. 1 (1990) 193–225) Alg. i Anal 1:1 (1989) 178–206.
D. Friedan and S. Shenker, The analytic geometry of two-dimensional conformal field theory, Nucl. Phys. B281 (1987) 509–545.
J. Fröhlich and T. Kerler, Quantum Groups, Quantum Categories and Quantum Field Theory, Lecture Notes in Math. 1542 Springer, Berlin et al., (1993)
J. Fuchs, A.N. Schellekens and C. Schweigert, Galois modular invariants of WZW models, Nucl. Phys. B437 (1995) 667–694.
P. Furlan, L.K. Hadjiivanov and I.T. Todorov, The price for quantum group symmetry: chiral versus 2D qZNW model, Trieste-Vienna preprint (1995).
P. Furlan, G.M. Sotkov and I.T. Todorov, Two-dimensional conformal quantum field theory, Riv. Nuovo Cim. 12:6 (1989) 1–202.
P. Furlan, Ya.S. Stanev and I.T. Todorov, Coherent state operators and n-point invariants for U q (sl(2)), Lett. Math. Phys. 22 (1991) 307–319.
A. Ch. Ganchev and V. B. Petkova, U q (sl (2)) invariant operators and minimal theory fusion matrices Phys. Lett. B233 (1989) 374–382.
T. Gannon, The classification of affine SU(3) modular invariant partition functions, Commun. Math. Phys. 161 (1994) 233–264.
K. Gawedzki, Geometry of Wess-Zumino-Witten model of conformal field theory, Nucl. Phys. B (Proc. Suppl.) 18B (1990) 78–91.
K. Gawedzki, Classical origin of quantum group symmetries in Wess-Zumino-Witten conformal field theory, Commun. Math. Phys. 139 (1991) 210–213.
K. Gawedzki, A. Kupiainen, SU(2) Chern Simons theory of genus zero, Comm. Math. Phys. 135 (1991) 531–546.
P. Goddard, D. Olive (eds.), Kac-Moody and Virasoro Algebras, A reprint volume for Physicists, World Scientific, Singapore (1988).
L.K. Hadjiivanov, R.R. Paunov and I.T. Todorov, Quantum group extended chiral p-models, Nucl. Phys. B356 (1991) 387–438.
M. Jimbo, A q-difference analogue of U(g) and the Yang-Baxter equation, Lett. Math. Phys. 10 (1985) 63–69.
M. Jimbo, A q-analogue of U(gl(N+1)), Hecke algebras and the Yang-Baxter equation, Lett. Math. Phys. 11 (1986) 247–252.
V.G. Kac, Infinite Dimensional Lie Algebras, Third edition, Cambridge Univ. Press, Cambridge, (1990).
V.G. Knizhnik and A.B. Zamolodchikov, Current algebra And Wess-Zumino model in two dimensions, Nucl. Phys. B247 (1984) 83–103.
R. de L. Kronig, Zur Neutrino Theorie des Lichtes III, Physica 2 (1935) 968–980.
G. Lusztig, Introduction to Quantum Groups, Progress in Mathematics v. 110 series eds. J. Oesterlé, A. Weinstein, Birkhäuser, Boston (1993).
G. Mack and V. Schomerus, Quasi Hopf quantum symmetry in quantum theory, Nucl. Phys. B370 (1992) 185–230.
L. Michel, Ya.S. Stanev and I.T. Todorov, D-E classification of the local extensions of the su 2 current algebras (Theor. Math. Phys. 92 (1993) 1063), Teor Mat. Fiz. 92 (1992) 507–521.
G. Moore and N. Seiberg, Classical and quantum conformal field theory, Commun. Math. Phys. 123 (1989) 177–254.
G. Moore and N. Seiberg, Lectures on RCFT, Superstrings 89, Proceedings of the Trieste 1989 Spring School, World Scientific Singapore (1990) 1–129.
K.-H. Rehren, Y.S. Stanev and I.T. Todorov, Characterizing invariants for local extensions of currents algebras, Hamburg-Vienna preprint DESY 94-164, ESI 132 (1994), hep-th/9409165, Commun. Math. Phys. (1995), to be published.
Ya.S. Stanev, Classification of the local extensions of the SU(3) chiral, current algebra, J. Math Phys. 36 (1995) 2053–2069.
Ya.S. Stanev, Classification of the local extensions of the SU(2)×SU(2) chiral current algebra, J. Math Phys. 36 (1995) 2070–2084.
Ya. S. Stanev, I.T. Todorov and L.K. Hadjiivanov, Braid invariant rational conformal models with a quantum group symmetry, Phys. Lett. B276 (1992) 87–94.
Ya.S. Stanev, I.T. Todorov and L.K. Hadjiivanov, Braid invariant chiral conformal models with a quantum group symmetry, Quantum Symmetries, ed. by H.-D. Doebner, V.K. Dobrev, World Scientific Singapore (1993), p. 24–40.
Ya. S. Stanev and I.T. Todorov, On Schwarz problem for the \(\widehat{su}_2\) Knizhnik-Zamolodchikov equation, Lett. Math. Phys., ESI preprint 121 (1994)
W. Thirring, A soluble relativistic field theory, Ann. Phys. (N.Y.) 3 (1958) 91–112.
I.T. Todorov, Infinite Lie algebras in 2-dimensional conformal field theory, Talk in: International Conference on Differential Geomtric methods in Theoretical Physics (Shumen, Bulgaria, August 1984), in Differential Geometric Methods in Theoretical Physics, H.-D. Doebner and T.D. Palev, Eds., World Scientific Singapore (1986) pp. 297–347.
I.T. Todorov, Current algebra approach to conformal invariant 2-dimensional models, Phys. Lett. B153 (1985) 77–81.
I.T. Todorov, What are we learning from 2-dimensional conformal models? in: Mathematical Physics Toward the 21st Century, R.N. Sen, A. Gersten, Eds., Ben Gurion University of the Negev Press, Beer Sheva (1994), pp. 160–176.
I.T. Todorov, Arithmetic features of rational conformal field theory, Ann. Inst. Poincaré, Bures-sur-Yvette preprint IHES/P/95/10.
I.T. Todorov and Ya. S. Stanev, Chiral Current Algebras and 2-Dimensional Conformal Models, Troisième Cycle de la Physique en Suisse Romande, Lausanne (1992).
S. Tomonaga, Remarks on Bloch's method of sound waves applied to manyfermion problems, Prog. Theor. Phys. 5 (1950) 544–569.
A. Tsuchiya and Y. Kanie, Vertex operators in the conformal field theory on P 1 and monodromy representations of the braid group, Lett. Math. Phys. 13 (1987) 303–312, Conformal field theory and solvable lattice modells, Advanced Studies in Pure Mathematics 16 (1988) 297–372.
E. Witten, Non-Abelian bosonization in two dimensions, Commun. Math. Phys. 92 (1984) 455–472.
A.B. Zamolodchikov and V.A. Fateev, Operator algebra and correlation functions in two-dimensional SU(2)xSU(2) chiral Wess-Zumino model, Yad.Fiz. 43 (1986) 1031–1044; transl.: Sov. J. Nucl. Phys. 43 (1986), 657–664.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag
About this paper
Cite this paper
Stanev, Y.S., Todorov, I.T. (1996). Monodromy representation of the mapping class group B n for the su 2 Knizhnik-Zamolodchikov equation. In: Grosse, H., Pittner, L. (eds) Low-Dimensional Models in Statistical Physics and Quantum Field Theory. Lecture Notes in Physics, vol 469. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0102558
Download citation
DOI: https://doi.org/10.1007/BFb0102558
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60990-2
Online ISBN: 978-3-540-49778-3
eBook Packages: Springer Book Archive