Farrokh Atai (Kobe University)
The deformed Calogero-Moser-Sutherland model and orthogonality of the super-Jack polynomials
17:00--18:30, August 1 (Wed), 2018
Room B314, Faculty of Science
The deformed Calogero-Moser-Sutherland (CMS) models were introduced as mathematically natural generalizations of the CMS models. Although the deformed CMS models share many of the mathematical properties of the CMS models, it proved more difficult to obtain a complete understanding of these deformed models and their corresponding eigenfunctions. In the first part of this seminar, I will present an overview of the different known deformed CMS models and then mainly discuss the trigonometric deformed CMS model (corresponding to A-type systems) and its exact eigenfunctions given in terms of the super-Jack polynomials. I will then present some recent results showing that the super-Jack polynomials are orthogonal with respect to a positive semi-definite, degenerate Hermitian product, which naturally generalizes Macdonald's inner product for the Jack polynomials, and give the corresponding (quadratic) norms explicitly. This seminar is based on joint work with M. Hallnäs and E. Langmann.