On Young's Orthogonal Form and the Characters of the Alternating Group
Patrick Headley
DOI: 10.1023/A:1022465117807
Abstract
A combinatorial method of determining the characters of the alternating group is presented. We use matrix representations, due to Thrall, that are closely related to Young”s orthogonal form of representations of the symmetric group. The characters are computed directly from matrix entries of these representations and entries of the character table of the symmetric group.
Pages: 127–134
Keywords: group character; alternating group; Young tableau
Full Text: PDF
References
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2. C. Greene, "A rational function identity related to the Murnaghan-Nakayama formula for the characters of Sn," J. Alg. Combin. 1 (1992), 235-255.
3. I.M. Isaacs, Character Theory of Finite Groups, Academic Press, San Diego, 1976.
4. G.D. James, The Representation Theory of the Symmetric Groups, Springer-Verlag, New York, 1978.
5. G.D. James and A. Kerber, The Representation Theory of the Symmetric Group, Addison-Wesley, Reading, MA, 1981.
6. D.B. Rutherford, Substitutional Analysis, Edinburgh University Press, 1948.
7. J.R. Stembridge, "On the eigenvalues of representations of reflection groups and wreath products," Pacific Journal of Mathematics 140 (1989), 353-396.
8. R.M. Thrall, "Young's semi-normal representation of the symmetric group," Duke Mathematical Journal 8 (1941), 611-624.