Groupes quantiques

Jean-Louis Verdier

Séminaire Bourbaki (1986-1987)

  • Volume: 29, page 305-319
  • ISSN: 0303-1179

How to cite

top

Verdier, Jean-Louis. "Groupes quantiques." Séminaire Bourbaki 29 (1986-1987): 305-319. <http://eudml.org/doc/110085>.

@article{Verdier1986-1987,
author = {Verdier, Jean-Louis},
journal = {Séminaire Bourbaki},
keywords = {quantum groups; quantum Yang-Baxter equations; quantum inverse scattering method},
language = {fre},
pages = {305-319},
publisher = {Société Mathématique de France},
title = {Groupes quantiques},
url = {http://eudml.org/doc/110085},
volume = {29},
year = {1986-1987},
}

TY - JOUR
AU - Verdier, Jean-Louis
TI - Groupes quantiques
JO - Séminaire Bourbaki
PY - 1986-1987
PB - Société Mathématique de France
VL - 29
SP - 305
EP - 319
LA - fre
KW - quantum groups; quantum Yang-Baxter equations; quantum inverse scattering method
UR - http://eudml.org/doc/110085
ER -

References

top
  1. [1] V.G. Drinfel'd - Quantum groups, Proc. ICM 86, Traduction russe : Zapiski Nauchny seminarov LOMI, vol. 155 (1986). Zbl0617.16004MR934283
  2. [2] R.J. Baxter - Exactly solved models, Academic Press, London, 1982. MR690578
  3. [3] A.A. Belavin, V.G. Drinfel'd - On the solutions of the classical Yang - Baxter equations, Funct. Anal. and its applic., 16 (1982) , 159-180. Zbl0511.22011MR674005
  4. [4] I.V. Cherednik - On "quantum" de formations of irreducible finite dimensional representations of glN , Dokl. Acad. Nauk CCCP, tome 287 (1986), n° 5 (en russe) et Sov. Math. Dokl. vol. 33 (1986), n° 2 (en anglais). Zbl0623.20030MR839706
  5. [5] V.G. Drinfel'd - Hamiltonian structures on Lie groups, Lie bialgebras and the meaning of the classical Yang - Baxter equations, Doklady, Ac. Nauk., CCCP, Tome 268 (1983), n° 2, Trad. anglaise : Soviet Math. Dokl., vol. 27 (1983), n° 1. Zbl0526.58017MR688240
  6. [6] V.G. Drinfel'd - Degenerate affine Hecke algebras and Yangians, Funk. Anal. i prilozen20 (1986), n° 1, 69-70 (en russe). Zbl0599.20049MR831053
  7. [7] I.M. Gelfand, I.V. Cherednik - Abstract Hamiltonian formalism for classical Yang - Baxter bundles, Uspehi Mat. Nauk, 38 (1983), n° 3, 3-21. Zbl0536.58006MR704634
  8. [8] M. Jaekel et J.-M. Maillard - Modèles exacts en Mécanique Statistique et modèles exactement solubles en Physique des Particules, in Mathématique et Physique, Séminaire de l'E.N.S.1979-1982, Progress in Mathematics, Birkhäuser, vol. 37 (1983). 
  9. [9] M. Jimbo - A q-analogue of U(gl(n+1)), Hecke algebra, and the Yang - Baxter equation, Letters in Math. Phys.11 (1986), 247-252. Zbl0602.17005MR841713
  10. [10] A.N. Kirillov, N. Yu. Reshetikhin - The Yangians, Bethe Ansatz and combinatorics, Letters in Math. Phys.12 (1986), 199-208. Zbl0643.20027MR865758
  11. [11] Y. Kosmann - Schwarzbach - Poisson - Drinfel'd groups, Proc. Oberwolfach Conference on non linear evolution equations (July 1986), M. Ablowitz, B. Fuchssteiner, M. Kruskal ed. World Scientific Publ. , à paraître. Zbl0726.58021MR900393
  12. [12] Yu I. Manin - Some remarks on Koszul algebras and quantum groups, Conférence en l'honneur de J.-L. Koszul, Juin 1987, à paraître. Zbl0625.58040MR927397
  13. [13] A.G. Reiman et M.A. Semenov-Tyan-Shansky - Hamiltonian structure of Kadomtsev - Petviashvili type equations, Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V.A. Steklova AN SSSR, Vol. 133, 212-227, 1984. Zbl0546.58031MR742159
  14. [14] M. Rosso - Comparaison des groupes SU(2) quantiques de Drinfel'd et de Woronowicz, CRAS t. 304, Série I, n° 12, 1987, 323-326. Zbl0617.16005MR889754
  15. [15] M.A. Semenov-Tyan-Shansky - Dressing transformations and Poisson group actions, Publication RIMS Kyoto Univ.21 (1986), n° 6. Zbl0673.58019MR842417
  16. [16] M.A. Semenov-Tyan-Shansky - Classical R-matrices, Lax equations, Poisson - Lie groups and dressing trans formations in Field theory, quantum gravity and strings, II, Lecture Notes in Physics, Springer Verlag, 280, 174- 214. Zbl0666.22010
  17. [17] E.K. Sklyanin - The quantum version of the inverse scattering method, Zapiski Nauch. Seminarov LOMI95 (1980), 55-128. Zbl0464.35071MR606022
  18. [18] S.L. Woronowicz - Compact matrix pseudogroups, Prépublication, Warsawa, 1987. MR901157
  19. [19] S.L. Woronowicz - Twisted SU(2) group : An example of non commutative differential calculus, à paraître dans RIMS Publ., Kyoto Univ. Zbl0676.46050
  20. [20] C.N. Yang - Some exact results for the many body problem in one dimension with repulsive delta function interaction, Phys. Rev. Letters, 19 (1967), n° 23, 1312-1314. Zbl0152.46301MR261870

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.