Graphical method for computing the determinant and inverse of a matrix. II. Generating functions for the (a<sub>n</sub>b<sub>n</sub>0 0...) representation matrices of SU(n)
J J Labarthe; J J Labarthe; Univ. Paris-XI, Orsay, France
Журнал:
Journal of Physics A: Mathematical and General
Дата:
1980-09-01
Аннотация:
For pt.I see ibid., vol.11, p.1009 (1978). Considers a special 2n*2n matrix 1-x for which the determinant is the square of a polynomial in the x<sub>ij</sub>. A graph G with n branches is associated to the matrix and det(1-x) and (1-x)<sub>ij</sub><sup>-1</sup> are expressed in terms of sums over subgraphs of G. The generating functions of the representation matrices D<sub>MM'</sub><sup>(m)</sup>(u) of the representations (m)=(a<sub>n</sub>b<sub>n</sub>0...) of SU(n) are expressed in terms of the determinant and inverse of such a 2n*2n matrix.
319.0Кб