Farrokh Atai (Kobe University) 

The deformed CalogeroMoserSutherland model and orthogonality of the
superJack polynomials 
17：0018：30, August 1 (Wed), 2018 
Room B314, Faculty of Science 

Abstract: 



The deformed CalogeroMoserSutherland (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 Atype systems) and its exact eigenfunctions given in
terms of the superJack polynomials. I will then present some recent results
showing that the superJack polynomials are orthogonal with respect to a
positive semidefinite, 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.


