1996-1996

N/A

link has been studied between all the different types of canonical bases Gelfand-Zeitlin for finite-dimensional irreducible representations of the quantum algebra Uq (su (3)). It was clearly shown that the coefficients of such a connection, called the Weyl coefficients are equal (up to a few simple factors) q-coefficients Cancer (or q-6j symbols) quantum algebra Uq (su (2)). He developed the theory of Clebsch-Gordan coefficients (Wigner) for the quantum algebra Uq (u (3)). The canonical solution to the problem of multiplicity in the tensor product of irreducible finite-dimensional representations of the algebra u (3), proposed Biedenharnom, Lauck and Hecht and implemented in computer codes Draerom and Akiyama, was generalized to the case of quantum algebra Uq (u (3)). The method of projection operators had obtained an analytical formula for the special ( "seed") Uq (u (3)) - Wigner coefficients. This result can be used which can be used in the circuit-Draera Akiyama for other Wigner coefficients normalized for the conventional algebra U (3) and for q-deformed algebra Uq (su (3)). They were calculated and tabulated all isoscalar factors such as <(22) '(22) || (lm)> q with unit multiplicity. Found a new two-parameter deformation of the universal enveloping algebra U (g [u]) for the Lie polynomial current algebra g [u] over any simple finite-dimensional complex Lie algebra g. It is shown that such a quantum Hopf algebra can be seen as quantization of U (g [u]) in the direction of classical r-matrix, which is the sum of the simplest rational and trigonometric solutions of the Yang-Baxter classical equation, depending on the parameters. Studied classical limit elliptic algebra Aq, p (sl2) and its variant limiting Ax, h (sl2). The corresponding Lie algebra is the central extension of the algebra sl2-valued generalized (doubly) - periodic functions. Classic elliptic and trigonometric solutions of the classical Yang-Baxter equation are interpreted in terms of Lie formalism Semenov-Tyan-Shan. Presenting geometric realization of the category of finite-dimensional representations of simple Lie algebra with a tensor structure defined monodromies solutions KZ equation (kvazitenzornoy Drinfeld category). It is proved that this kvazitenzornaya category equivalent to the category of factoring modules over the ring More... »

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2 | ″ | schema:description | link has been studied between all the different types of canonical bases Gelfand-Zeitlin for finite-dimensional irreducible representations of the quantum algebra Uq (su (3)). It was clearly shown that the coefficients of such a connection, called the Weyl coefficients are equal (up to a few simple factors) q-coefficients Cancer (or q-6j symbols) quantum algebra Uq (su (2)). He developed the theory of Clebsch-Gordan coefficients (Wigner) for the quantum algebra Uq (u (3)). The canonical solution to the problem of multiplicity in the tensor product of irreducible finite-dimensional representations of the algebra u (3), proposed Biedenharnom, Lauck and Hecht and implemented in computer codes Draerom and Akiyama, was generalized to the case of quantum algebra Uq (u (3)). The method of projection operators had obtained an analytical formula for the special ( "seed") Uq (u (3)) - Wigner coefficients. This result can be used which can be used in the circuit-Draera Akiyama for other Wigner coefficients normalized for the conventional algebra U (3) and for q-deformed algebra Uq (su (3)). They were calculated and tabulated all isoscalar factors such as <(22) '(22) || (lm)> q with unit multiplicity. Found a new two-parameter deformation of the universal enveloping algebra U (g [u]) for the Lie polynomial current algebra g [u] over any simple finite-dimensional complex Lie algebra g. It is shown that such a quantum Hopf algebra can be seen as quantization of U (g [u]) in the direction of classical r-matrix, which is the sum of the simplest rational and trigonometric solutions of the Yang-Baxter classical equation, depending on the parameters. Studied classical limit elliptic algebra Aq, p (sl2) and its variant limiting Ax, h (sl2). The corresponding Lie algebra is the central extension of the algebra sl2-valued generalized (doubly) - periodic functions. Classic elliptic and trigonometric solutions of the classical Yang-Baxter equation are interpreted in terms of Lie formalism Semenov-Tyan-Shan. Presenting geometric realization of the category of finite-dimensional representations of simple Lie algebra with a tensor structure defined monodromies solutions KZ equation (kvazitenzornoy Drinfeld category). It is proved that this kvazitenzornaya category equivalent to the category of factoring modules over the ring |

3 | ″ | schema:endDate | 1996-12-31T00:00:00Z |

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11 | ″ | ″ | Clebsch-Gordan coefficients |

12 | ″ | ″ | Hecht |

13 | ″ | ″ | Lauck |

14 | ″ | ″ | Lie algebra |

15 | ″ | ″ | Lie formalism Semenov-Tyan |

16 | ″ | ″ | Lie polynomial current algebra g |

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20 | ″ | ″ | Shan |

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22 | ″ | ″ | Weyl coefficients |

23 | ″ | ″ | Wigner |

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28 | ″ | ″ | analytical formula |

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30 | ″ | ″ | canonical bases Gelfand-Zeitlin |

31 | ″ | ″ | canonical solution |

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35 | ″ | ″ | circuit-Draera Akiyama |

36 | ″ | ″ | classical Yang-Baxter equation |

37 | ″ | ″ | classical limit |

38 | ″ | ″ | coefficient |

39 | ″ | ″ | coefficients Cancer |

40 | ″ | ″ | computer codes Draerom |

41 | ″ | ″ | connection |

42 | ″ | ″ | conventional algebra U |

43 | ″ | ″ | deformed algebra Uq |

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46 | ″ | ″ | elliptic algebra Aq |

47 | ″ | ″ | factoring modules |

48 | ″ | ″ | few simple factors |

49 | ″ | ″ | finite-dimensional irreducible representations |

50 | ″ | ″ | finite-dimensional representations |

51 | ″ | ″ | geometric realization |

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53 | ″ | ″ | isoscalar factors |

54 | ″ | ″ | kvazitenzornaya category |

55 | ″ | ″ | kvazitenzornoy Drinfeld category |

56 | ″ | ″ | link |

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58 | ″ | ″ | monodromies solutions KZ equation |

59 | ″ | ″ | multiplicity |

60 | ″ | ″ | other Wigner coefficients |

61 | ″ | ″ | parameters |

62 | ″ | ″ | periodic functions |

63 | ″ | ″ | problem |

64 | ″ | ″ | projection operators |

65 | ″ | ″ | q-6j symbols |

66 | ″ | ″ | quantization |

67 | ″ | ″ | quantum Hopf algebra |

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69 | ″ | ″ | quantum physics |

70 | ″ | ″ | results |

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75 | ″ | ″ | sum |

76 | ″ | ″ | tensor product |

77 | ″ | ″ | tensor structure |

78 | ″ | ″ | terms |

79 | ″ | ″ | theory |

80 | ″ | ″ | trigonometric solutions |

81 | ″ | ″ | two-parameter deformation |

82 | ″ | ″ | unit multiplicity |

83 | ″ | ″ | variants |

84 | ″ | schema:name | New group-theoretic methods in quantum physics |

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