CONTENTS -- Preface -- Index Theory for Wiener-Hopf Operators on Convex Cones A. Alldridge -- 1. Wiener-Hopf Operators on the Half Line -- 1.1. Problem and Classical Solution -- 1.2. C* -Algebraic Reformulation -- 2. Composition Series for the Wiener-Hopf Algebra -- 2.1. Multivariate Wiener-Hop! Operators -- 2.2. Groupoid C* -Algebras -- 2.3. An Application of Groupoid C"-Algebras -- 2.4. The Wiener-Hop! Algebra as a Groupoid C"-Algebra -- 2.5. The Composition Series -- 3. Index Theory for the Wiener-Hopf Algebra -- 3.1. Analytical Index -- 3.2. A Connecting Bibundle -- 4. The Case of Polyhedral Cones -- 4.1. Cellular Differential and Index Maps -- 4.2. Atiyah-Hirzebruch Spectral Sequence -- References -- A Variant of the Frobenius Reciprocity for Restricted Representations on Nilpotent Lie Groups A. Baklouti, H. Fujiwara and 1. Ludwig -- 1. Introduction -- 2. Backgrounds -- 2.1. Some notations and basic facts -- 2.2. The orbit theory -- 2.3. Induced and restricted representations -- 2.4. Coexponential bases -- 2.5. Fmbenius vectors -- 3. The main result -- 4. Proof of the main result -- 5. Examples -- 5.1. On threadlike nilpotent Lie groups -- 5.2. An eight dimensional nilpotent Lie group -- Acknowledgements -- References -- Mehler Hemigroups and Embedding of Discrete Skew Convolution Semigroups on Simply Connected Nilpotent Lie Groups P. Becker-Kern and W. Hazod -- 1. Introduction -- 2. Results on finite-dimensional vector spaces -- 3. Hemigroup embedding -- 4. Space-time enlargement and Mehler hemigroups -- 5. Representations by generalized Lie-Trotter formulas -- References -- Transforms, Polynomials and Integrable Models Associated with Reflection Groups C. F. Dunkl -- 1. Introduction -- 2. Intertwining operator and an integral transform -- 3. Group-theoretic aspects of V and K -- 4. Intertwining operator for the group B2.

5. Quantum-mechanical models -- 6. Nonsymmetric Jack polynomials -- Acknowledgments -- References -- Positive and Negative Definite Functions on a Hypergroup and Its Dual H. Heyer -- Preface -- 1. Introduction -- 2. Bounded positive definite functions -- 2.1. The dual space of a hypergroup -- 2.2. The Bochner-Weil and Levy theorems -- 3. Strongly positive definite functions in the commutative case -- 3.1. Dual space and dual hypergroup -- 3.2. The Bochner and Levy theorems -- 4. Strongly negative definite functions in the commutative case -- 4.1. The Schoenberg correspondence -- 4.2. Local Sturm-Liouville hypergroups -- 4.3. Levy-Khintchine decomposition -- 5. Conditionally positive definite functions -- 5.1. Cocycles and co boundaries -- 5.2. Accompanying arrays -- 5.3. Infinitely divisible positive definite functions -- References -- Symbolic Dynamics for the Geodesic Flow on Locally Symmetric Orbifolds of Rank One 1. Hilgert and A. D. Pohl -- 1. Introduction -- 2. Symbolic dynamics -- 3. Cusp expansions -- 3.1. Associated transfer operators -- 3.2. The case of the modular surface -- 4. Outlook -- References -- Towards Projective Representations and Spin Characters of Finite and Infinite Complex Reflection Groups T. Hirai, E. Hirai and A. Hora -- 1. Wreath product groups and complex reflection groups -- 1.1. Wreath products 6 n {T) and their canonical subgroups -- 1.2. Complex reflection groups and their inductive limits -- 2. Characters of factor representations of a group -- 2.1. Some generalities for characters of factor representations -- 2.2. Chamcter formula for wreath products 6 00 (T) and its canonical subgroups -- 3. Generality for projective representations -- 3.1. Schur multiplier H2(G,e X ) and representation groups -- 3.2. Case of 6 n , ~n and 6 -- 4. Representation groups of complex reflection groups.

4.1. Schur multiplier and representation groups of Weyl groups -- 4.2. Representation groups of generalized symmetric groups -- 4.3. Representation groups of G(m,p, n) = 6 n (Z ... )S(p) -- 5. Structure of R(G(m,l,n») and R(G(m,l,oo») -- 6. Properties of spin characters of generalized symIlletric groups G(m,l,n) and G(m,l,oo) -- References -- An Irreducible Homogeneous Non-Selfdual Cone of Arbitrary Rank Linearly Isomorphic to the Dual Cone H. Ishi and T. Nomura -- 1. Introduction -- 2. Description of the cone -- 3. Dual cone -- References -- Extensions of Commutative Hypergroups S. Kawakami -- 1. Introduction -- 2. Preliminaries -- 3. Splitting extensions of hypergroups -- 4. Non-splitting extensions of hypergroups -- 5. Cohomological approach to the extension problem on hypergroups -- References -- Real Hardy Space for Jacobi Analysis and Its Applications T. Kawazoe -- 1. Introduction -- 2. Notations -- 3. A key relation -- 4. Real Hardy spaces -- 5. Littlewood-Paley g-function -- 6. Lusin area function -- References -- A Remark on Random Groups of the Triangular Model T. Kondo -- 1. Introduction -- 2. CAT(O) spaces -- References -- Asymptotic Behaviour of Quantum Markov Processes B. K iimmerer -- 1. From Graphs to Markov Processes -- 1.1. An Example -- 1.2. Road-Coloured Graphs and Markov Processes -- 1.3. Synchronizing Words -- 1.4. Outlook -- 2. Markov Processes from Road-Coloured Graphs in Operator Algebras -- 2.1. Markov Processes from Road-Coloured Graphs -- 2.2. Algebraization -- 2.3. Quantization -- 3. Synchronising Words and Asymptotic Completeness -- 3.1. Asymptotic Completeness -- 3.2. Synchronizing Words for Countable State Spaces -- 4. Synchronizing Words and Preparation of States -- 4.1. Preparation of States -- 4.2. Two-Sided Quantum Markov Processes -- 4.3. The Micro-Maser and Preparation of Quantum States -- Acknowledgement.

References -- On a-amenability of Commutative Hypergroups R. Lasser -- 1. Introduction -- 2. Preliminaries and a-amenability -- 3. Convergence to cp-invariance -- 4. Examples and comments -- References -- Moments of Characteristic Polynomials of a Random Matrix Associated with Compact Symmetric Spaces S. Matsumoto -- 1 Introduction -- 2 Dyson's circular ensembles -- 2.1 Definition of circular ,a-ensembles -- 2.1.1 COE ({3 = 1) -- 2.1.2 CUE (f3 = 2) -- 2.1.3 CSE ((3 = 4) -- 2.1.4 Quaternion expression for CSE matrices -- 2.2 Jack polynomials -- 2.2.1 Partitions -- 2.2.2 Definition of Jack polynomials -- 2.3 Characteristic polynomial average -- 3 Jacobi ensembles -- 3.1 Definition of Jacobi ensembles -- 3.2 Heckman and Opdam's Jacobi polynomials -- 3.3 Characteristic polynomial average -- 4 Closing remarks -- References -- Semi-bounded Unitary Representations of Infinite-Dimensional Lie Groups K.-H. Neeb -- Introduction -- 1. Semi-equicontinuous convex sets -- 2. Momentum sets of smooth unitary representations -- 3. Bounded representations -- 4. The abelian case -- References -- A Note on the Capelli Identities for Symmetric Pairs of Hermitian Type K. Nishiyama and A. Wachi -- 1. Introduction -- 2. Case C -- 2.1. Formulas for the Weil representation -- 2.2. Capelli identity for Case

2. Bessel functions on matrix cones -- 3. Radial analysis on matrix spaces, integral formulas, and Hankel transforms -- 4. Hypergroups -- 5. Bessel hypergroups on matrix cones -- 6. Wishart-distributions and probabilistic aspects -- 7. Bessel functions associated with root system Bq -- 8. Hypergroups on the Weyl chamber -- Acknowledgments -- References -- Irreducible Decompositions of Unitary Representations and Extremal Decompositions of Positive-Definite Functions on Groups H. Shimomura -- 1. INTRODUCTION -- 2. IRREDUCIBLE DECOMPOSITIONS OF UNITARY REPRESENTATIONS OF INFINITE DIMENSIONAL GROUPS -- 2.1 Presentation of the basic results. -- 2.2 Representations of the group of diffeomorphisms on M. -- 2.3 Specific examples of realization. -- 3. IRREDUCIBLE DECOMPOSITIONS OF UNITARY REPRESENTATIONS AND EXTEREMAL DECOMPOSITIONS OF PDF -- 3.1 Presentation of the problem. -- 3.2 Main results -- 3.3 Characters on the infinite permutation group, and their disintegrations. -- REFERENCES -- Ensembles of Hermitian Random Matrices Associated to Symmetric Spaces M. Stolz -- 1. Introduction -- 2. A Wigner-type theorem -- 2.1. A proof of Theorem 1.1 -- 2.2. Extensions -- 3. Invariant ensembles and large deviations -- Acknowledgement -- References -- Limit Theorems for Radial Random Walks on Homogeneous Spaces with Growing Dimensions M. Voit -- 1. Introduction -- 2. Radial limit theorems on jRP for p ---* 00 -- 3. Radial limit theorems on the matrix spaces Mp,q for p --+ 00 -- 4. A central limit theorem for hyperbolic spaces and Jacobi convolutions on [0, oc[ -- References.