Invariant Differential Operators for Non-Compact Lie Groups: the Sp(n,R) Case
Abstract
In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebras sp(n,R), in detail for n=6. Our choice of these algebras is motivated by the fact that they belong to a narrow class of algebras, which we call 'conformal Lie algebras', which have very similar properties to the conformal algebras of Minkowski space-time. We give the main multiplets and the main reduced multiplets of indecomposable elementary representations for n=6, including the necessary data for all relevant invariant differential operators. In fact, this gives by reduction also the cases for n<6, since the main multiplet for fixed n coincides with one reduced case for n+1.
Keywords
Cite
@article{arxiv.1205.5521,
title = {Invariant Differential Operators for Non-Compact Lie Groups: the Sp(n,R) Case},
author = {V. K. Dobrev},
journal= {arXiv preprint arXiv:1205.5521},
year = {2017}
}
Comments
Latex2e, 27 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:0812.2690, arXiv:0812.2655