Monodromy representations of braid groups and Yang-Baxter equations
Annales de l'institut Fourier (1987)
- Volume: 37, Issue: 4, page 139-160
- ISSN: 0373-0956
Access Full Article
topAbstract
topHow to cite
topKohno, Toshitake. "Monodromy representations of braid groups and Yang-Baxter equations." Annales de l'institut Fourier 37.4 (1987): 139-160. <http://eudml.org/doc/74770>.
@article{Kohno1987,
abstract = {Motivated by the two dimensional conformal field theory with gauge symmetry, we shall study the monodromy of the integrable connections associated with the simple Lie algebras. This gives a series of linear representations of the braid group whose explicit form is described by solutions of the quantum Yang-Baxter equation.},
author = {Kohno, Toshitake},
journal = {Annales de l'institut Fourier},
keywords = {two-dimensional conformal field theory; gauge symmetry; integrable connections; simple Lie algebras},
language = {eng},
number = {4},
pages = {139-160},
publisher = {Association des Annales de l'Institut Fourier},
title = {Monodromy representations of braid groups and Yang-Baxter equations},
url = {http://eudml.org/doc/74770},
volume = {37},
year = {1987},
}
TY - JOUR
AU - Kohno, Toshitake
TI - Monodromy representations of braid groups and Yang-Baxter equations
JO - Annales de l'institut Fourier
PY - 1987
PB - Association des Annales de l'Institut Fourier
VL - 37
IS - 4
SP - 139
EP - 160
AB - Motivated by the two dimensional conformal field theory with gauge symmetry, we shall study the monodromy of the integrable connections associated with the simple Lie algebras. This gives a series of linear representations of the braid group whose explicit form is described by solutions of the quantum Yang-Baxter equation.
LA - eng
KW - two-dimensional conformal field theory; gauge symmetry; integrable connections; simple Lie algebras
UR - http://eudml.org/doc/74770
ER -
References
top- [1] K. AOMOTO, Fonctions hyperlogarithmiques et groupes de monodromie unipotents, J. Fac. Sci. Tokyo, 25 (1978), 149-156. Zbl0416.32020MR80g:14016
- [2] J. BIRMAN, Braids, links, and mapping class groups, Ann. Math. Stud., 82 (1974).
- [3] A. A. BELAVIN and V. G. DRINFEL'D, Solutions of the classical Yang-Baxter equation for simple Lie algebras, Funct. Anal. Appl., 16 (1982), 1-29. Zbl0504.22016MR84e:81034
- [4] N. BOURBAKI, Groupes et algèbres de Lie, IV, V, VI, Masson, Paris (1982). Zbl0483.22001
- [5] A. A. BELAVIN, A. N. POLYAKOV and A. B. ZAMOLODCHIKOV, Infinite dimensional symmetries in two dimensional quantum field theory, Nucl. Phys., B241 (1984), 333-380. Zbl0661.17013MR86m:81097
- [6] K. T. CHEN, Iterated path integrals, Bull. Amer. Math. Soc., 83 (1977), 831-879. Zbl0389.58001MR56 #13210
- [7] V. G. DRINFEL'D, Quantum groups, preprint, ICM Berkeley (1986). Zbl0617.16004
- [8] R. HAIN, On a generalization of Hilbert 21st problem, Ann. ENS, 49 (1986), 609-627. Zbl0616.14004MR89a:14013
- [9] M. JIMBO, A q-difference analogue of U(g) and Yang-Baxter equation, Lett. in Math. Phys., 10 (1985), 63-69. Zbl0587.17004MR86k:17008
- [10] M. JIMBO, Quantum R matrix for the generalized Toda system, Comm. Math. Phys., 102 (1986), 537-547. Zbl0604.58013MR87h:58086
- [11] M. JIMBO, A q-analogue of U(gl(N + 1)), Hecke algebra, and the Yang-Baxter equation. Lett. in Math. Phys., 11 (1986), 247-252. Zbl0602.17005MR87k:17011
- [12] M. JIMBO, Quantum R matrix related to the generalized Toda system : an algebraic approach, Lect. Note in Phys., 246 (1986), Springer. Zbl0604.58013MR87j:17013
- [13] V. JONES, Index of subfactors, Invent. Math., 72 (1983), 1-25. Zbl0508.46040MR84d:46097
- [14] V. JONES, Hecke algebra representations of braid groups and link polynomials, Ann. of Math., 126 (1987), 335-388. Zbl0631.57005MR89c:46092
- [15] V. G. KAC, Infinite dimensional Lie algebras, Progress in Math., 44, Birkhäuser (1983). Zbl0537.17001MR86h:17015
- [16] T. KOHNO, Série de Poincaré-Koszul associée aux groupes de tresses pures, Invent. Math., 82 (1985), 57-75. Zbl0574.55009MR87c:32015a
- [17] T. KOHNO, Linear representations of braid groups and classical Yang-Baxter equations, to appear in Contemp. Math., "Artin's braid groups". Zbl0661.20026
- [18] V. G. KNIZHNIK and A. B. ZAMOLODCHIKOV, Current algebra and Wess-Zumino models in two dimensions, Nucl. Phys., B247 (1984), 83-103. Zbl0661.17020MR87h:81129
- [19] J. MORGAN, The algebraic topology of smooth algebraic varieties, Publ. IHES, 48 (1978), 103-204. Zbl0401.14003
- [20] J. MURAKAMI, On the Jones invariant of paralleled links and linear representations of braid groups, preprint (1986).
- [21] D. SULLIVAN, Infinitesimal computations in topology, Publ. IHES, 47 (1977), 269-331. Zbl0374.57002MR58 #31119
- [22] A. TSUCHIYA and Y. KANIE, Vertex operators in two dimensional conformal field theory on P1 and monodromy representations of braid groups, preprint (1987), to appear in Adv. Stud. In Pure Math. Zbl0631.17010
- [23] J. L. VERDIER, Groupes quantiques, Séminaire Bourbaki, 1987 juin.
- [24] H. WENZL, Representations of Hecke algebras and subfactors, Thesis, Univ. of Pensylvenia (1985).
Citations in EuDML Documents
top- Christian Kassel, Monodromie des systèmes de Knizhnik-Zamolodchikov et groupes quantiques
- Olivier Mathieu, Équations de Knizhnik-Zamolodchikov et théorie des représentations
- Alberto Benvegnù, Mauro Spera, Low-Dimensional Pure Braid Group Representations Via Nilpotent Flat Connections
- Richard M. Hain, The Hodge de Rham theory of relative Malcev completion
- Ivan Marin, Quotients infinitésimaux du groupe de tresses
- Tu Quoc Thang Le, Jun Murakami, The universal Vassiliev-Kontsevich invariant for framed oriented links
- Claudio Procesi, Complementi di sottospazi e singolarità coniche
- Marc Rosso, Représentations des groupes quantiques
- Pierre Cartier, Jacobiennes généralisées, monodromie unipotente et intégrales itérées
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.