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Quantum Groups

Proceedings of Workshops held in the Euler International Mathematical Institute, Leningrad, Fall 1990

  • Conference proceedings
  • © 1992

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Editors:
  1. Petr P. Kulish
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1510)

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Table of contents (36 papers)

  1. Front Matter

    Pages I-XII
    Download chapter PDF

  2. On some unsolved problems in quantum group theory

    • V. G. Drinfeld
    Pages 1-8

  3. Quantum symmetry

    • Murray Gerstenhaber, Anthony Giaquinto, Samuel D. Schack
    Pages 9-46

  4. Yang-Baxter equation and deformation of associative and Lie algebras

    • D. Gurevich, V. Rubtsov
    Pages 47-55

  5. Quantum G-spaces and Heisenberg algebra

    • L. I. Korogodsky, L. L. Vaksman
    Pages 56-66

  6. Real and imaginary forms of quantum groups

    • Vladimir Lyubashenko
    Pages 67-78

  7. Rank of quantum groups and braided groups in dual form

    • Shahn Majid
    Pages 79-89

  8. Yangians of the “strange” lie superalgebras

    • M. L. Nazarov
    Pages 90-97

  9. Askey-wilson polynomials as spherical functions on SU q(2)

    • Masatoshi Noumi, Katsuhisa Mimachi
    Pages 98-103

  10. Twisted yangians and infinite-dimensional classical Lie algebras

    • G. I. Olshanskii
    Pages 104-119

  11. Differential graded Lie algebras, quasi-hopf algebras and higher homotopy algebras

    • Jim Stasheff
    Pages 120-137

  12. Quantum deformation of the flag variety

    • Earl J. Taft
    Pages 138-141

  13. Zonal spherical functions on quantum symmetric spaces and MacDonald's symmetric polynomials

    • Kimio Ueno, Tadayoshi Takebayashi
    Pages 142-147

  14. Hidden quantum groups inside Kac-Moody algebras

    • A. Alekseev, L. Faddeev, M. Semenov-Tian-Shansky
    Pages 148-158

  15. Liouville theory on the lattice and universal exchange algebra for bloch waves

    • O. Babelon
    Pages 159-175

  16. Non-local currents in 2D QFT: An alternative to the quantum inverse scattering method

    • Denis Bernard, André Leclair
    Pages 176-196

  17. Induced representations and tensor operators for quantum groups

    • L. C. Biedenharn, M. A. Lohe
    Pages 197-209

  18. Affine toda field theory: S-matrix vs perturbation

    • H. W. Braden, E. Corrigan, P. E. Dorey, R. Sasaki
    Pages 210-220

  19. Contractions of quantum groups

    • E. Celeghini, R. Giachetti, E. Sorace, M. Tarlini
    Pages 221-244

  20. New solutions of Yang-Baxter equations and quantum group structures

    • Mo-Lin Ge
    Pages 245-258
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Keywords

About this book

The theory of Quantum Groups is a rapidly developing area with numerous applications in mathematics and theoretical physics, e.g. in link and knot invariants in topology, q-special functions, conformal field theory, quantum integrable models. The aim of the Euler Institute's workshops was to review and compile the progress achieved in the different subfields. Near 100 participants came from 14 countries. More than 20 contributions written up for this book contain new, unpublished material and half of them include a survey of recent results in the field (deformation theory, graded differential algebras, contraction technique, knot invariants, q-special functions). FROM THE CONTENTS: V.G. Drinfeld: On Some Unsolved Problems in Quantum Group Theory.- M. Gerstenhaber, A. Giaquinto, S.D. Schack: Quantum Symmetry.- L.I. Korogodsky,L.L. Vaksman: Quantum G-Spaces and Heisenberg Algebra.-J. Stasheff: Differential Graded Lie Algebras, Quasi-Hopf Algebras and Higher Homotopy Algebras.- A.Yu. Alekseev, L.D. Faddeev, M.A. Semenov-Tian-Shansky: Hidden Quantum Groups inside Kac-Moody Algebras.- J.-L. Gervais: Quantum Group Symmetry of 2D Gravity.- T. Kohno: Invariants of 3-Manifolds Based on Conformal Field Theory and Heegaard Splitting.- O. Viro: Moves of Triangulations of a PL-Manifold.

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