U. Haifa Algebra seminar: Thursday, Oct 27, 2022. Speaker: Sergey Khoroshkin (IITP Moscow). Title: “Wave functions of hyperbolic Sutherland model”.

There will be a Special Algebra seminar on Thursday, Oct 27, 2022 01:00 PM Jerusalem

In-person, in room 614 of the Science & Education Building, University of Haifa,

Speaker:    Sergey Khoroshkin (IITP Moscow)
Title: Wave functions of hyperbolic Sutherland model.


Following arXiv:2108.04895, 2108.05393
Any special function is an eigenfunction of  differential or difference operators: 

In this way, Calogero – Sutherland differential operators stand behind the theory of Jack symmetric functions. On the noncompact side of the story, they are radial parts of Laplace operators on symmetric spaces for special values of the coupling constant, and in these cases group, theoretical methods can be used for the precise description of the corresponding wave functions (zonal spherical functions). 

I show how these results, including ‘contiguous’ difference relations on spectral variables, can be generalized to other values of the parameters. 

The exposition uses classical techniques from representation theory: matrix elements, and Gelfand-Zetlin formulas, which all will be explained in elementary language.