Beschreibung
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.
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E-Mail: juergen.hartmann@springer.com
