ISSN:
1573-0530
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract Schur's lemma and the properties of circular matrices are used to establish a necessary and sufficient condition for the finite-dimensional irreducible matrix representations of an arbitrary groupG to admit real coupling (or Clebsch-Gordan) coefficients. The Pontryagin-Van Kampen and Tannaka-Krein duality theorems are found to be of considerable value in implementing the condition, which requires that complex conjugation effects an automorphism on the group of all matrices having the same reduction of their tensor products as the matrix representations ofG. This result is noted to be relevant to a generalization of the Frobenius-Schur invariant.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00704579
