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On the Representation Theory of the Symmetric Groups

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Abstract

We present here a new approach to the description of finite-dimensional complex irreducible representations of the symmetric groups due to A. Okounkov and A. Vershik. It gives an alternative construction to the combinatorial one, which uses tabloids, polytabloids, and Specht modules. Its aim is to show how the combinatorial objects of the theory (Young diagrams and tableaux) arise from the internal structure of the symmetric group. Bibliography: 9 titles.

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REFERENCES

  1. P. Diaconis, “Application of noncommutative Fourier analysis to probability problems,” Lect. Notes Math., 1362, 51–100 (1988).

    Google Scholar 

  2. A. Okounkov and A. Vershik, “A new approach to representation theory of symmetric groups,” Selecta Math., New Ser., 2, 581–605 (1996).

    Google Scholar 

  3. J. Friedman, “On Cayley graphs on the symmetric group generated by transpositions,” Combinatorica, 20, 505–519 (2000).

    Google Scholar 

  4. J. Friedman and P. Hanlon, “On the Betti numbers of chessboard complexes,” J. Algebraic Combin., 8, 193–203 (1996).

    Google Scholar 

  5. A. M. Odlyzko, L. Flatto, and D. B. Wales, “Random shuffles and group representation,” Ann. Probab., 13, 587–598 (1985).

    Google Scholar 

  6. G. I. Olshanski, “Extension of the algebra U(g) for in finite-dimensional classical Lie algebras g and the Yangians Y (gl (m)),” Soviet. Math. Dokl., 36, 569–573 (1988).

    Google Scholar 

  7. B. Sagan, The Symmetric Group. Representations, Combinatorial Algorithms, and Symmetric Functions, 2nd edition, Springer-Verlag, New York (2001).

    Google Scholar 

  8. F. Scarabotti, “Radon transforms on the symmetric group and harmonic analysis of a class of invariant Laplacians,” Forum Math., 10, 407–411 (1998).

    Google Scholar 

  9. J.-P. Serre, Representations Lineaires des Groupes Finis, Hermann, Paris (1967).

    Google Scholar 

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Authors and Affiliations

  1. Ecole Normale Superieure de Lyon, France

    P. Py

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  1. P. Py
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 301, 2003, pp. 229–242.

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Py, P. On the Representation Theory of the Symmetric Groups. J Math Sci 129, 3806–3813 (2005). https://doi.org/10.1007/s10958-005-0316-7

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  • DOI: https://doi.org/10.1007/s10958-005-0316-7

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