论文信息 - An Introduction to Group Representations and Orthogonal Polynomials

An Introduction to Group Representations and Orthogonal Polynomials

An elementary non-technical introduction to group representations and orthogonal polynomials is given. Orthogonality relations for the spherical functions for the rotation groups in Euclidean space (ultraspherical polynomials), and the matrix elements of SU(2) (Jacobi polynomials) are discussed. A general theory for finite groups acting on graphs, giving a finite set of discrete orthogonal polynomials is given. Explicit examples include graphs giving the Krawtchouk and Hahn polynomials.

Dennis Stanton

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