Lie Theory and Special Functions

A(exp addition theorem analytic basis analytic functions basis functions basis vectors Bessel functions Chapter Clebsch–Gordan coefficients cohomology class commutation relations complex variables computation confluent hypergeometric coordinates corresponding defined differential equations differential operators effective realization expression factorization follows form a basis form an orthonormal ga's given Hilbert space hypergeometric functions identity element induced infinitesimal operators inner product irreducible representations irreducible unitary representations isomorphic Jºf Jºh JºJº Laguerre functions Laguerre polynomials Lemma Lie derivatives Lie group local Lie group mapping matrix elements multiplier representation nonnegative integer nonzero obtain operators T(g orthonormal basis recursion relations representation D(u representation of SL(2 representation theory satisfy the commutation Section ſº solution special function theory subalgebra subspace T(exp tion transformation group type A operators unitary irreducible representations valid vectors f verify