On * -representations of the Hopf * -algebra associated with the quantum group U q ( n )

H. Tjerk Koelink

Compositio Mathematica (1991)

  • Volume: 77, Issue: 2, page 199-231
  • ISSN: 0010-437X

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Koelink, H. Tjerk. "On $*$-representations of the Hopf $*$-algebra associated with the quantum group $U_q(n)$." Compositio Mathematica 77.2 (1991): 199-231. <http://eudml.org/doc/90072>.

@article{Koelink1991,
author = {Koelink, H. Tjerk},
journal = {Compositio Mathematica},
keywords = {compact quantum groups; star operation; Verma modules; representations; compact matrix pseudogroup; type I -algebra},
language = {eng},
number = {2},
pages = {199-231},
publisher = {Kluwer Academic Publishers},
title = {On $*$-representations of the Hopf $*$-algebra associated with the quantum group $U_q(n)$},
url = {http://eudml.org/doc/90072},
volume = {77},
year = {1991},
}

TY - JOUR
AU - Koelink, H. Tjerk
TI - On $*$-representations of the Hopf $*$-algebra associated with the quantum group $U_q(n)$
JO - Compositio Mathematica
PY - 1991
PB - Kluwer Academic Publishers
VL - 77
IS - 2
SP - 199
EP - 231
LA - eng
KW - compact quantum groups; star operation; Verma modules; representations; compact matrix pseudogroup; type I -algebra
UR - http://eudml.org/doc/90072
ER -

References

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  5. 5 Faddeev, L.D., N. Yu, Reshetikhin and L.A. Takhtajan, Quantization of Lie groups and Lie algebras, in 'Algebraic Analysis', vol. 1 (eds. M. Kashiwara and T. Kawai), Academic Press, 1988, 129-139. Zbl0677.17010MR992450
  6. 6 Humphreys, J.E., Introduction to Lie algebras and representation theory, GTM 9, Springer Verlag, 1972. Zbl0254.17004MR323842
  7. 7 Jimbo, M., A q-difference analogue of U(g) and the Yang-Baxter equation, Lett. Math. Phys.10, 1985, 63-69. Zbl0587.17004MR797001
  8. 8 Knapp, A.W., Representation theory of semisimple groups, Princeton University Press, 1986. Zbl0604.22001MR855239
  9. 9 Koornwinder, T.H., Orthogonal polynomials in connection with quantum groups, in 'Orthogonal Polynomials: Theory and Practice' (ed. P. Nevai), NATO ASI Series C, Vol. 294, Kluwer, 1990, 257-292. Zbl0697.42019MR1100297
  10. 10 Mackey, G.W., The theory of unitary group representations, The University of Chicago Press, 1976. Zbl0344.22002MR396826
  11. 11 Manin, Yu. I., Quantum groups and non-commutative geometry, Centre de Recherches Mathématiques, Université de Montreal, 1988. Zbl0724.17006
  12. 12 Parshall, B. and J.-P. Wang, Quantum linear groups I, preprint, 1989. MR1048073
  13. 13 Reshetikhin, N. Yu., L.A. Takhtajan and L.D. Faddeev, Quantification of Lie groups and Lie algebras, Algebra i Analiz1, 1989, 178-206. (In Russian.) Zbl0715.17015
  14. 14 Rosso, M., An analogue of P. B. W. theorem and the universal R-matrix for Uhsl(N + 1), Comm. Math. Phys.124, 1989, 307-318. Zbl0694.17006MR1012870
  15. 15 Rudin, W., Functional analysis, Tata McGraw-Hill, 1974. Zbl0253.46001
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  17. 17 Sweedler, M.E., Hopf algebras, Benjamin, 1969. Zbl0194.32901MR252485
  18. 18 Takesaki, M., Theory of operator algebras I, Springer Verlag, 1979. Zbl0436.46043
  19. 19 Vaksman, L.L. and Ya. S. Soibelman, Function algebra on the quantum group SU(2), Funktsional Anal. i. Prilozhen22 (3), 1988, 1-14,English translation in Functional Anal. Appl.22(3), 1988, 170-181. Zbl0679.43006MR961757
  20. 20 Woronowicz, S.L., Twisted SU(2) group. An example of a non-commutative differential calculus, Publ. Res. Inst. Math. Sci.23, 1987, 117-181. Zbl0676.46050MR890482
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  23. 23 Yamane, H., A Poincaré-Birkhoff-Witt theorem for the quantum group of type AN, Proc. Japan Acad.64, Ser. A, 1988, 385-386. Zbl0677.17011MR979952

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