Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-20T01:23:58.207Z Has data issue: false hasContentIssue false
  • English
  • Français

Linear Symmetry Classes

Published online by Cambridge University Press:  20 November 2018

L. J. Cummings  and
R. W. Robinson
L. J. Cummings
Affiliation:
University of Waterloo, Waterloo, Ontario
R. W. Robinson
Affiliation:
University of Newcastle, New South Wales, Australia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A formula is derived for the dimension of a symmetry class of tensors (over a finite dimensional complex vector space) associated with an arbitrary finite permutation group G and a linear character of x of G. This generalizes a result of the first author [3] which solved the problem in case G is a cyclic group.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 6 , 01 December 1976 , pp. 1311 - 1319
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Botta, P. and Williamson, S. G., Unitar similarity of symmetry operators, Linear Algebra and Appl. 3 (1970), 249–256.Google Scholar
2. Burnside, W., Theory of groups of finite order, 2nd ed. (Cambridge Univ. Press, London, 1911, reprinted by Dover, N.Y., 1955).Google Scholar
3. Cummings, L. J., Cyclic symmetry classes, J. of Algebra 40 (1976), 401–405.Google Scholar
4. Gauss, K. F., Disquisitiones Arithmeticae, Trans. Clarke, A. A. (Yale Univ. Press, New Haven, 1965).Google Scholar
5. Klass, M. J., A generalization of Burnside1 s combinatorial lemma, J. Comb. Theory (Ser. A) 20 (1976), 273–278.Google Scholar
6. Marcus, M. and Mine, H., Generalized matrix functions, Trans. Amer. Math. Soc. 116 (1965), 316–329.Google Scholar
7. Merris, R. and Pierce, S., Elementary divisors of higher degree associated transformations, Linear and Multilinear Algebra 1 (1973), 241–250.Google Scholar
8. Pierce, S., Orthogonal decompositions of tensor spaces, J. Res. Nat. Bur. Stand. (U.S.) 74B (1970), 41–44.Google Scholar
9. Rudvalis, A. and Snapper, E., Numerical polynomials for arbitrary characters, J. Comb. Theory 10 (1971), 145–159.Google Scholar
10. Stockmeyer, P. J., Enumeration of graphs with prescribed automorphism group, Ph.D. Thesis, University of Michigan, Ann Arbor, Mich., 1971.Google Scholar
11. Weyl, H., Der Zusammenhang Zwischen der Symmetrischen und der Lineare Gruppe, Ann. of Math. SO (1929), 499–516.Google Scholar
12. White, D. E., Counting patterns with a given automorphism group, Proc. Amer. Math. Soc. 47 (1975), 41–44.Google Scholar