Representation of Lie Groups and Special Functions

This is the second of three major volumes which present a comprehensive treatment of the theory of the main classes of special functions from the point of view of the theory of group representations. This volume deals with the properties of special functions, and the relation of orthogonal polynomials (Legendre, Gegenbauer, Jacobi, Laguerre, Bessel and others) to class I representations of various groups. The tree method for the construction of bases for representation spaces is provided. “Continuous” bases in the spaces of functions on hyperboloids and cones and corresponding Poisson kernels are found. The properties of the g-analogs of classical orthogonal polynomials, related to representations of the Chevalley groups, and of special functions connected with fields of p-adic numbers, are examined. Subscribers to the complete set of three volumes will be entitled to a discount of 15%.