Annals of Combinatorics 1 (1997) 91-98


Young's Natural Idempotents as Polynomials

Alain Lascoux

Université de Marne-la-Vallée, Institut Gaspard Monge, 2 rue de la Butte Verte 93166 Noisy-le-Grand Cedex, France
Alain.Lascoux@univ-mlv.fr

Received January 27, 1997

AMS Subject Classification: 05E10, 20C30

Abstract. Coding permutations as monomials, one obtains a compact expression of representatives of Young's natural idempotents for the symmetric group, or of q-idempotents in the Hecke algebra.

Keywords: Young, idempotents


References

1.  R. Dipper and G. James, Representations of Hecke algebras of general linear groups, Proc. London Math. Soc. 52 (1986) 20–52.

2.  G. Duchamp and S. Kim, Intertwining Spaces Associated with q-analogues of the Young Symmetrizers in the Hecke Algebra 36, Banach Center Publications, Warszawa, 1996, pp. 61–70.

3.  G. Duchamp, D. Krob, A. Lascoux, B. Leclerc, Y. Scharf and J.-Y. Thibon, Euler-Poincarè characteristic and polynomial representation of Iwahori-Hecke algebra, Pub. RIMS 31 (1995) 179–201.

4.  G.D. James and A. Kerber, The Representation Theory of the Symmetric Group, Addison-Wesley, 1981.

5.  A. Lascoux and M.P. Schützenberger, Symmetry and flag manifold, In: Invariant Theory, Lecture Notes in Math. 996, Springer-Verlag, Berlin-Heidelberg-New York, 1983, pp. 118–144.

6.  A. Lascoux and M.P. Schützenberger, Symmetrisation operators on polynomial rings, Funct. Anal i prigogi 21 (1987) 77–78.

7.  I.G. Macdonald, Symmetric Functions and Hall Polynomials, Clarendon Press, Oxford, 1979.

8.  D.E. Rutherford, Substitutional Analysis, Edinburgh University Press, 1948.

9.  A. Young, Collected Papers of Alfred Young 1873-1940, University of Toronto Press, 1977.

10.  S. Veigneau, ACE, an algebraic combinatorics environment for the computer algebra system MAPLE, Thesis, Chapter 1, Universitè de Marne La Vallèe, France, 1996.


Get the LaTeX | DVI | PS file of this abstract.

back