Algebraic Structures and Operators Calculus Volume III: Representations of Lie Groups (Repost)

Introduction I. General remarks . 1 II. Notations . . 5 III. Lie algebras: some basics . 8 Chapter 1 Operator calculus and Appell systems I. Boson calculus . 17 II. Holomorphic canonical calculus . . 18 III. Canonical Appell systems . . 23 Chapter 2 Representations of Lie groups I. Coordinates on Lie groups . . . 28 II. Dual representations. 29 III. Matrix elements. . . 37 IV. Induced representations and homogeneous spaces . . 40 General Appell systems Chapter 3 I. Convolution and stochastic processes . 44 II. Stochastic processes on Lie groups . . 46 III. Appell systems on Lie groups. . 49 Chapter 4 Canonical systems in several variables I. Homogeneous spaces and Cartan decompositions . . 54 II. Induced representation and coherent states . 62 III. Orthogonal polynomials in several variables . 68 Chapter 5 Algebras with discrete spectrum I. Calculus on groups: review of the theory .. 83 II. Finite-difference algebra . 85 III. q-HW algebra and basic hypergeometric functions .. 89 IV. su2 and Krawtchouk polynomials .. . 93 V. e2 and Lommel polynomials . . 101 Chapter 6 Nilpotent and solvable algebras I. Heisenberg algebras . .. 113 II. Type-H Lie algebras .. 118 Vll III. Upper-triangular matrices .. . 125 IV. Affine and Euclidean algebras . . 127 Chapter 7 Hermitian symmetric spaces I. Basic structures . 131 II. Space of rectangular matrices . . 133 III. Space of skew-symmetric matrices . . 136 IV. Space of symmetric matrices . 143 Chapter 8 Properties of matrix elements I. Addition formulas .. . 147 II. Recurrences . .. 148 III. Quotient representations and summation formulas .. 149 Chapter 9 Symbolic computations I. Computing the pi-matrices . . 153 II. Adjoint group .. 154 III. Recursive computation of matrix elements .