Bulg. J. Phys. vol.35 no.s1 (2008), pp. 372-399



Intertwining Operators for the Schrödinger Algebra in n ≥ 3 Space Dimensions

N. Aizawa1, V.K. Dobrev2, H.-D. Doebner3, S. Stoimenov2
1Department of Mathematics and Information Sciences, Graduate School of Science, Osaka Prefecture University, Daisen Campus, Sakai, Osaka 590-0035, Japan
2Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tsarigradsko Chaussee, 1784 Sofia, Bulgaria
3Department of Physics, Metallurgy and Material Science, Technical University Clausthal, 38678 Clausthal-Zellerfeld, Germany
Abstract. Hierarchies of equations invariant under Schrödinger algebras ŝ(n) in (n+1) dimensional space-time are constructed using the singular vectors in Verma modules. For general n, the singular vectors are found for a particular case, while for the physical case n = 3 the influence of so(3) part in Schrödinger algebra is investigated. The result is a composite singular vector and more general form of the invariant equations.

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