Abstract
A new proof of the hook formula for the dimension of representations of the symmetric group is given with the help of identities which are of independent interest. A probabilistic interpretation of the proof and new formulas relating the parameters of the Young diagrams are given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
G. James, Theory of Representations of Symmetric Groups [Russian translation], Moscow (1982).
J. Frame, G. Robinson, and R. Thrall, “The hook graph of the symmetric group,” Can. J. Math.,6, 316–324 (1954).
D. Knuth, The Art of Programming [Russian translation], Vol. 3, Moscow (1978).
P. A. MacMahon, Combinatorial Analysis, Vol. 2, Chelsea, N.Y. (1960).
C. Greene, A. Nijenhuis, and H. Wilf, “Another probabilistic method in the theory of Young tableaux,” J. Combin. Theory, Ser. A,37, 127–135 (1984).
A. M. Vershik and S. V. Kerov, “Locally semisimple algebras, combinatorial theory and the K-functor,” Itogi Nauki Tekhn., Ser. Sovrem. Probl. Matem., Nov. Dostizh.,26, 3–56 (1985).
A. M. Vershik and S. V. Kerov, “Asymptotic Plancherel measures of the symmetric group,” Dokl. Akad. Nauk SSSR,233, No. 6, 1024–1027 (1977).
A. M. Vershik, “Local stationary algebras,” in: Proceedings of the First Siberian School on Algebra and Analysis, Kemerovo, 1987; Dep. VINITI, Moscow (1988).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Akad. Nauk SSSR, Vol. 172, pp. 3–20, 1989.
Rights and permissions
About this article
Cite this article
Vershik, A.M. Hook formula and related identities. J Math Sci 59, 1029–1040 (1992). https://doi.org/10.1007/BF01480684
Issue Date:
DOI: https://doi.org/10.1007/BF01480684