2.2 Representation Theory, Operator Algebras and Complex Analysis

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 mathematical physics.
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.
Study of quantum groups connects via deformation quantization and quantum groupoids to mathematical physics.
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.