Symmetric Lie superalgebras and deformed quantum Calogero-Moser problems
Representation Theory
2015-03-27 v2 Mathematical Physics
math.MP
Abstract
The representation theory of symmetric Lie superalgebras and corresponding spherical functions are studied in relation with the theory of the deformed quantum Calogero-Moser systems. In the special case of symmetric pair g=gl(n,2m), k=osp(n,2m) we establish a natural bijection between projective covers of spherically typical irreducible g-modules and the finite dimensional generalised eigenspaces of the algebra of Calogero-Moser integrals D_{n,m} acting on the corresponding Laurent quasi-invariants A_{n,m}.
Keywords
Cite
@article{arxiv.1412.8768,
title = {Symmetric Lie superalgebras and deformed quantum Calogero-Moser problems},
author = {A. N. Sergeev and A. P. Veselov},
journal= {arXiv preprint arXiv:1412.8768},
year = {2015}
}
Comments
Extended version with minor corrections. A section with an explicit analysis of the simplest case m=n=1 is added