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Unitary Symmetry and Combinatorics

Unitary Symmetry and Combinatorics PDF Author: James D. Louck
Publisher: World Scientific
ISBN: 9812814736
Category : Mathematics
Languages : en
Pages : 642

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Book Description
This monograph integrates unitary symmetry and combinatorics, showing in great detail how the coupling of angular momenta in quantum mechanics is related to binary trees, trivalent trees, cubic graphs, MacMahon''s master theorem, and other basic combinatorial concepts. A comprehensive theory of recoupling matrices for quantum angular momentum is developed. For the general unitary group, polynomial forms in many variables called matrix Schur functions have the remarkable property of giving all irreducible representations of the general unitary group and are the basic objects of study. The structure of these irreducible polynomials and the reduction of their Kronecker product is developed in detail, as is the theory of tensor operators.