A method is derived for obtaining the tensor covariants of the finite groups, belonging to any given factor system, starting from an arbitrary tensor of rank r in a N-dimensional vector space. The transformation properties of the irreducible tensor operators for the projective representations of the group have been discussed. The Wigner-Eckart theorem for these representations has also been studied.

1.
P.
Rudra
,
J. Math. Phys.
6
,
1273
(
1965
). We shall refer to this paper as I.
2.
Iu. I.
Sirotin
,
Dokl. Akad. Nauk SSSR
133
,
321
(
1960
)
[English transl.:
Iu. I.
Sirotin
,
Soviet Phys.‐Doklady
5
,
774
(
1961
)].
3.
G. F.
Smith
,
J. Math. Phys.
5
,
1612
(
1964
).
4.
P.
Erdös
,
Helv. Phys. Acta
37
,
493
(
1964
).
5.
M. E. Rose, Elementary Theory of Angular Momentum (John Wiley & Sons, Inc., New York, 1957).
6.
U. Fano and G. Racah, Irreducible Tensorial Set (Academic Press, Inc., New York, 1959).
7.
H. Weyl, Classical Groups (Princeton University Press, Princeton, New Jersey, 1946).
8.
H. Weyl, The Theory of Groups and Quantum Mechanics (Dover Publications, Inc., New York) (English transl.)
9.
E. P. Wigner, Group Theory and its Application to the Quantum Mechanics of Atomic Spectra (Academic Press, Inc., New York, 1959) (English transl.).
10.
M. Hamermesh, Group Theory and its Application to Physical Problems (Addison‐Wesley Publishing Company, Inc. Reading, Massachusetts, 1962).
11.
J.
Ginibre
,
J. Math. Phys.
4
,
720
(
1963
).
12.
G. E.
Baird
and
L. C.
Biedenharn
,
J. Math. Phys.
5
,
1730
(
1964
).
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