Abstract
We have obtained all the finite-dimensional unitary irreps of gl(m|n) and C(n), which also exhaust such irreps of all the basic classical Lie superalgebras. The lowest weights of such irreps are worked out explicitly. It is also shown that the contravariant and covariant tensor irreps of gl(m|n) are unitary irreps of type (1) and type (2) respectively, explaining the applicability of the Young diagram method to these two types of tensor irreps.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
KacV. G., Adv. Math. 26, 8 (1977); Lecture Notes in Math 676, Springer, Berlin, 1978, p. 597.
ScheunertM., NahmW., and RittenbergV., J. Math. Phys. 18, 146 (1977).
Gould, M. D. and Zhang, R. B., Classification of all star and grade star irreps of gl(m|1), Queensland Univ. Preprint, May, 1989.
Zhang, R. B. and Gould, M. D., Classification of all star and grade star irreps of C(n), Queensland Univ. Preprint, May, 1989.
Gould, M. D. and Zhang, R. B., Classification of all star irreps of gl(m|n), Queensland Univ. Preprint, August, 1989.
Van derJeugtJ., J. Math. Phys. 26, 913 (1985).
BalantekinA. B. and BarsI., J. Math. Phys. 22, 1149 (1981); 23, 1239 (1982).
DondiP. H. and JarvisP. D., J. Phys. A14, 547 (1981).
FarmerR. J. and JarvisP. D., J. Phys. A16, 473 (1983); A17, 2365 (1984); Hurni, J. P., J. Phys. A20, 57755 (1987); Berele, A. and Regev, A., Adv. Math. A64, 118 (1987).
WybourneB. G., J. Phys. A17, 1573 (1984).
HughesJ. W. B., J. Math. Phys. 22, 245 (1981); Ann. Israel Phys. Soc. 3, 320 (1980); Van der Jeugt, J., J. Math. Phys. 25, 3334 (1984); 28, 758 (1987); Heidenreich, W., Phys. Lett. B110, 461 (1982); Scheunert, M., Nahm, W., and Rittenberg, V., J. Math. Phys. 18, 155 (1977).