## L. D. Faddeev's Seminar on Mathematical PhysicsProfessor L. D. Faddeev's seminar at Steklov Mathematical Institute (St. Petersburg, Russia) has a record of more than 30 years of intensive work which has helped to shape modern mathematical physics. This collection, honoring Professor Faddeev's 65th anniversary, has been prepared by his students and colleagues. Topics covered in the volume include classical and quantum integrable systems (both analytic and algebraic aspects), quantum groups and generalizations, quantum field theory, and deformation quantization. Included is a history of the seminar highlighting important developments, such as the invention of the quantum inverse scattering method and of quantum groups. The book will serve nicely as a comprehensive, up-to-date resource on the topic. |

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### Contents

Some personal historic notes on our seminar | 1 |

Incidence matrix description of intersecting pbrane solutions | 19 |

A discrete time Lagrange top and discrete elastic curves | 39 |

The GelfandLevitanMarchenko equation and the longtime asymptotics | 63 |

From the tetrahedron equation to universal Rmatrices | 79 |

Quantum inverse scattering method and correlation functions | 115 |

Drinfeld twists and algebraic Bethe Ansatz | 137 |

Darboux transformations covariance theorems and integrable systems | 179 |

Generalized qdeformed GelfandDickey structures on the group | 211 |

Deformation quantization of Kähler manifolds | 257 |

rmatrix approach I | 277 |

Completeness of the hypergeometric solutions of the qkZ equation at level | 309 |

### Common terms and phrases

action algebra applications approach arbitrary associated assume asymptotic bracket classical coefficients commutative completely consider construction corresponding Darboux defined definition deformation denote depend derivatives described determinant diagonal differential discrete discuss elements equal equation equivalent example exists expression F-matrices factorizing field finite fixed formal formula function give given Hamiltonian Hence identity integral introduce invariant inverse Lagrange lattice LEMMA limit linear manifold Math Mathematical matrix means method motion namely natural nonlinear notation Note obtain operator p-branes parameter particular Phys Physics Poisson polynomials potential present problem PROOF properties PROPOSITION prove quadratic quantization quantum R-matrix relations REMARK represent representation respect result satisfies simple solutions space spectral structure symbols symmetries Theorem theory transformation triangular twist universal values variables vector zeros