On Trees and Characters
Avital Frumkin
, Gordon James
and Yuval Roichman
DOI: 10.1023/A:1025052922664
Abstract
A new family of trees, defined in term of Young diagrams, is introduced. Values of central characters of the symmetric group are represented as a weighted enumeration of such trees. The proof involves a new decomposition theorem for representations corresponding to general shapes.
Pages: 323–334
Keywords: symmetric groups; central characters
Full Text: PDF
References
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2. G. Frobenius, \ddot Uber die Charaktere der Symmetrischen Gruppe, Berliner Berichte, 1900, pp. 516-534.
3. A. Goupil, D. Poulalhon, and G. Schaeffer, “Central characters and conjugacy classes of the symmetric group, or on some conjectures of J. Katriel,” Formal Power Series and Algebraic Combinatorics (Moscow 2000), Springer, Berlin, 2000, pp. 238-249.
4. R.E. Ingram, “Some characters of the symmetric group,” Proc. Amer. Math. Soc. 1 (1950), 358-369.
5. G.D. James and A. Kerber, “The representation theory of the symmetric group,” Encyclopedia of Math. and its Appl., Addison-Wesley, 1981, Vol. 16.
6. G.D. James and M.H. Peel, “Specht series for skew representations of symmetric groups,” J. Algebra 56 (1979), 343-364.
7. A. Lubotzky, “Discrete groups, expanding graphs and invariant measures,” Progress in Math., Birkh\ddot auser Verlag, 1994, Vol. 125.
8. V. Reiner and M. Shimozono, “Specht series for column-convex diagrams,” J. Algebra 174 (1995), 489-522.
9. Y. Roichman, “Characters of the symmetric groups: Recursive formulas, estimates and applications,” Emerging Applications of Number Theory, IMA Math. App., Springer, 1999, Vol. 109, pp. 525-546.
10. B.E. Sagan, The Symmetric Group. Representations, Combinatorial Algorithms, and Symmetric Functions, Wadsworth & Brooks/Cole, CA, 1991.
11. R.P. Stanley, Enumerative Combinatorics, Volume II. Cambridge University Press, Cambridge, 1999.
12. M. Suzuki, “The values of irreducible characters of the symmetric group,” The Arcata Conference on Representations of Finite Groups, Amer. Math. Soc. Proceedings of Symposia in Pure Mathematics, 1987, Vol. 47- Part 2, pp. 317-319.