Geodesic
Linear Symmetry Classes
Canadian journal of mathematics, Tome 28 (1976) no. 6, pp. 1311-1319

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Cummings, L. J.; Robinson, R. W. Linear Symmetry Classes. Canadian journal of mathematics, Tome 28 (1976) no. 6, pp. 1311-1319. doi: 10.4153/CJM-1976-130-0
@article{10_4153_CJM_1976_130_0,
     author = {Cummings, L. J. and Robinson, R. W.},
     title = {Linear {Symmetry} {Classes}},
     journal = {Canadian journal of mathematics},
     pages = {1311--1319},
     year = {1976},
     volume = {28},
     number = {6},
     doi = {10.4153/CJM-1976-130-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1976-130-0/}
}
TY  - JOUR
AU  - Cummings, L. J.
AU  - Robinson, R. W.
TI  - Linear Symmetry Classes
JO  - Canadian journal of mathematics
PY  - 1976
SP  - 1311
EP  - 1319
VL  - 28
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1976-130-0/
DO  - 10.4153/CJM-1976-130-0
ID  - 10_4153_CJM_1976_130_0
ER  - 
%0 Journal Article
%A Cummings, L. J.
%A Robinson, R. W.
%T Linear Symmetry Classes
%J Canadian journal of mathematics
%D 1976
%P 1311-1319
%V 28
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1976-130-0/
%R 10.4153/CJM-1976-130-0
%F 10_4153_CJM_1976_130_0

[1] 1. Botta, P. and Williamson, S. G., Unitar similarity of symmetry operators, Linear Algebra and Appl. 3 (1970), 249–256. Google Scholar

[2] 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] 3. Cummings, L. J., Cyclic symmetry classes, J. of Algebra 40 (1976), 401–405. Google Scholar

[4] 4. Gauss, K. F., Disquisitiones Arithmeticae, Trans. Clarke, A. A. (Yale Univ. Press, New Haven, 1965). Google Scholar

[5] 5. Klass, M. J., A generalization of Burnside1 s combinatorial lemma, J. Comb. Theory (Ser. A) 20 (1976), 273–278. Google Scholar

[6] 6. Marcus, M. and Mine, H., Generalized matrix functions, Trans. Amer. Math. Soc. 116 (1965), 316–329. Google Scholar

[7] 7. Merris, R. and Pierce, S., Elementary divisors of higher degree associated transformations, Linear and Multilinear Algebra 1 (1973), 241–250. Google Scholar

[8] 8. Pierce, S., Orthogonal decompositions of tensor spaces, J. Res. Nat. Bur. Stand. (U.S.) 74B (1970), 41–44. Google Scholar

[9] 9. Rudvalis, A. and Snapper, E., Numerical polynomials for arbitrary characters, J. Comb. Theory 10 (1971), 145–159. Google Scholar

[10] 10. Stockmeyer, P. J., Enumeration of graphs with prescribed automorphism group, Ph.D. Thesis, University of Michigan, Ann Arbor, Mich., 1971. Google Scholar

[11] 11. Weyl, H., Der Zusammenhang Zwischen der Symmetrischen und der Lineare Gruppe, Ann. of Math. SO (1929), 499–516. Google Scholar

[12] 12. White, D. E., Counting patterns with a given automorphism group, Proc. Amer. Math. Soc. 47 (1975), 41–44. Google Scholar

Cité par Sources :