English

Exceptional Lie Algebra $E_{7(-25)}$ (Multiplets and Invariant Differential Operators)

High Energy Physics - Theory 2023-09-06 v4 Representation Theory

Abstract

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact exceptional algebra E7(25)E_{7(-25)}. Our choice of this particular algebra is motivated by the fact that it belongs to a narrow class of algebras, which we call 'conformal Lie algebras', which have very similar properties to the conformal algebras of nn-dimensional Minkowski space-time. This class of algebras is identified and summarized in a table. Another motivation is related to the AdS/CFT correspondence. We give the multiplets of indecomposable elementary representations, including the necessary data for all relevant invariant differential operators.

Keywords

Cite

@article{arxiv.0812.2690,
  title  = {Exceptional Lie Algebra $E_{7(-25)}$ (Multiplets and Invariant Differential Operators)},
  author = {V. K. Dobrev},
  journal= {arXiv preprint arXiv:0812.2690},
  year   = {2023}
}

Comments

20 pages, 2 figures, TEX with input files harvmac.tex, amssym.def, amssym.tex; v2: added references; v3: change of normalization in f-lae (4.1) and (4.7); v4 corrected misprint. arXiv admin note: substantial text overlap with arXiv:0812.2655

R2 v1 2026-06-21T11:51:57.732Z