Abstract
The present paper is part of the project of systematic construction of invariant differential operators of noncompact semisimple Lie algebras. Here we give a summary of all multiplets containing physically relevant representations including the minimal ones for the algebra su(4, 4). Due to the recently established parabolic relations the results are valid also for the algebras sl(8, R) and su*(8)
Similar content being viewed by others
References
V. K. Dobrev, Rev. Math. Phys. 20, 407–449 (2008).
V. K. Dobrev, J. Phys. A 42, 285203 (2009).
V. K. Dobrev, Phys. At. Nucl. 76, 983–990 (2013).
V. K. Dobrev, J. High Energy Phys. 13, 02 (2013).
Harish-Chandra, Am. J. Math. 77, 743–777 (1955).
R. P. Langlands, “On the classification of irreducible representations of real algebraic groups,” in Mathematical Surveys and Monographs, Vol. 31 (Am. Math. Soc., Providence, 1988), pp. 101–170; IAS Preprint (1973).
D. P. Zhelobenko, Harmonic Analysis on Semisimple Complex Lie Groups (Nauka, Moscow, 1974) [in Russian].
A. W. Knapp and G. J. Zuckerman, Ann. Math. 116, 389–501 (1982).
V. K. Dobrev, G. Mack, V. B. Petkova, S. G. Petrova, and I. T. Todorov, Lect. Notes Phys. 63 (1977).
V. K. Dobrev, Rep. Math. Phys. 25, 159–181 (1988); ICTP Preprint IC/1986/393 (1986).
V. K. Dobrev, Lett. Math. Phys. 9, 205–211 (1985).
I. N. Bernstein, I. M. Gel’fand, and S. I. Gel’fand, Funct. Anal. Appl. 5, 1–8 (1971).
J. Dixmier, Enveloping Algebras (North Holland, New York, 1977).
A. W. Knapp and E. M. Stein, Ann. Math. 93, 489–578 (1971).
Author information
Authors and Affiliations
Corresponding author
Additional information
The article is published in the original.
Rights and permissions
About this article
Cite this article
Dobrev, V.K. Invariant differential operators for non-compact Lie groups: Summary of su(4,4) multiplets. Phys. Part. Nuclei Lett. 14, 277–285 (2017). https://doi.org/10.1134/S154747711702008X
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S154747711702008X