Algebraic Geometry. Proc. conf. Tokyo, Kyoto, 1982 by M. Raynaud, T. Shioda

By M. Raynaud, T. Shioda

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Erence that the number of possible symmetry groups now is larger. erent two-dimensional vibrational problems is given in Pavlov-Verevkin and Zhilinskii (1988a) (see also Zhilinskii, 1989b). In the simplest case of a non-linear AB molecule the image of the C group in the axial vector  T representation spanned by the components of the vibrational angular momentum constructed from two stretching modes, and , with symmetries A and B is the C group (Pavlov     Verevkin and Zhilinskii 1988a; Zhilinskii, 1989b).

The modi"cation of a control parameter J will eliminate the presence of a degeneracy point in the classical limit and will destroy the symmetry of the quantum energy levels. Are there any general rules for such modi"cations? We turn now to this question. 2. Isolated vibrational components and their rotational structure We initially assumed in the preceding subsection that the rotational multiplet associated with the non-degenerate vibrational state has 2J#1 energy levels for given quantum number J of the angular momentum.

Fig. 18 shows the convergence to the theoretical limit for tetrahedral molecules AB .  A constructive proof of Eq. (59) can be given if for each "nite group G and , we take  generating functions g ( ) for all possible irreducible representations of G and transform them into explicit expressions for N (N). To realize such a transformation some more information about high N behavior of the numbers of states is needed. Particularly important is the separation of the expression for the number of states into regular and oscillatory parts.

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