The Fourth Conference on Infinite Dimensional Harmonic Analysis brought together experts in harmonic analysis, operator algebras and probability theory. This volume includes articles that deal with the limit behavior of systems with many degrees of freedom in the presence of symmetry constraints.

A Variant of the Frobenius Reciprocity for Restricted Representations on Nilpotent Lie Groups (A Baklouti et al.); Transforms, Polynomials and Integrable Models Associated with Reflection Groups (C F Dunkl); Positive and Negative Definite Functions on Hypergroup and Its Dual (H Heyer); Towards Projective Representations and Spin Characters of Finite and Infinite Complex Reflection Groups (T Hirai et al.); Extensions of Commutative Hypergroups (S Kawakami); Semi-bounded Unitary Representations of Infinite Dimensional Lie Groups (K-H Neeb); Limit Theorems for Radial Random Walks on Homogeneous Spaces with Growing Dimensions (M Voit); and other papers.