2.2 Representation Theory,
Operator Algebras and Complex Analysis
E.M. Opdam, J.J.O.O. Wiegerinck
Description of the programme.
The cornerstones of this programme are Lie theory, special functions,
analytic aspects of modern mathematical physics, and complex analysis.
Interrelations between these areas are emphasized in the programme. In
particular, there are important links from Lie theory to special functions and to
Topics in Lie theory range from analytic to algebraic
and comprise analysis on semisimple Lie groups, semisimple symmetric spaces
and quantum groups. Study of (q)-special functions living on (quantum) groups
naturally links to multivariable functions associated with root systems like
Macdonald polynomials and Heckman-Opdam hypergeometric functions.
quantum groups connects via deformation quantization and quantum groupoids to
Work in the programme on one-variable special
functions and orthogonal polynomials uses many techniques from classical
analysis, and also emphasizes the development of computer algebra algorithms.
Work in complex analysis, mainly in several complex variables, is
in interplay with function algebras and functional analysis.