New group-theoretic methods in quantum physics View Homepage


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YEARS

1999-1999

FUNDING AMOUNT

N/A

ABSTRACT

(I) to get a detailed description of the quantum affine superalgebra $ U_q (\ hat {osp} (1 | 2)) $. It is shown that in this supercase can use the concept of the action of the braid group associated with the Weyl group. It is also shown that the q-analogue of the Cartan-Weyl basis for $ U_q (\ hat {osp} (1 | 2)) $ has a simple symmetry properties with respect to the action of the braid group. By using a clear structure of the q-analogue of the Cartan-Weyl basis and its properties in relation to the action of the braid group for the first time received a complete list of the commutation relations of this basis. In terms of the basis is a compact expression for the universal R-matrix and the projection operator. (Ii) It is shown that in the case of the second non-standard management solutions of the Yang-Baxter classical equations of the Lie algebra $ sl (2) $ explicitly there is a twist element, and that the corresponding quantum object is a deformation $ Yangian Y _ {\ eta} (sl ( 2)) $. (Iii) constructed monomial bases for the irreducible representations of the quantum algebra $ U_q (su (3)) $ and found the connection of these bases between themselves and with the q-analogue of the canonical basis of the Gelfand-Tsetlin. Received tensor form q-analogue of the canonical basis and found the action degrees of generators of the algebra in it. These results will be used in the future as the most important elements in the derivation of the general analytical formulas for the Clebsch-Gordan coefficients (CGC) of the algebra $ U_q (su (3)) $ in terms of the q-analogues 3j, 6j, 9j-symbols of the quantum algebra $ U_q (su (2)) $. (Iv) It has been shown that the previously proposed in the framework of the previous project (RFBR 96-01-1421) method of separating multiple irreducible representations of the quantum algebra $ U_q (su (3)) $ by diagonalization Gram matrices is effective for rather complex irreducible representations and multiplicities. For the first time a series of tabulated CGC type $ _ {q} $. (V) the first time it is shown that a well-known method Nikiforova- Suslov-Uvarova in the theory of classical orthogonal polynomials of a discrete variable on arbitrary non-uniform grids is equivalent to the method of Schrödinger factorization. Built-dimensional finite-difference equation on a triangular grid, allowing factored into the decision as the product of 2 polynomials Khan. (Vi) the first time we solve ur-tion Dirac Coulomb potential in a discrete representation (lagerrovsky basis) for the discrete and continuous spectra. (Vii) It was shown that the spectrum of the type of asymmetrical rigid rotator levels can be obtained within the extended algebraic model of interacting bosons with dynamical symmetry $ su (3) $. More... »

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http://www.rfbr.ru/rffi/ru/project_search/o_74224

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