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Higher Specht polynomials for the symmetric group. (English) Zbl 0811.20011
Let \(H\) be the regular \(S_ n\) module over the rationals. The authors of the announcement under review sketch a combinatorial algorithm for constructing a basis of \(H\) using pairs of standard Young tableaux. This construction allows them to construct bases of the irreducible components of \(H\).

MSC:
20C30 Representations of finite symmetric groups
05E05 Symmetric functions and generalizations
05E10 Combinatorial aspects of representation theory
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[1] A. M. Garsia and C. Procesi: On certain graded Sn-modules and the #-Kostk; polynomials. Adv. Math., 94, 82-138 (1992). · Zbl 0797.20012 · doi:10.1016/0001-8708(92)90034-I
[2] I. G. Macdonald : Symmetric Functions and Hall Polynomials. Oxford Universit: Press (1979). · Zbl 0899.05068
[3] I. G. Macdonald : Notes on Schubert Polynomials. Universite de Quebec a Montreal (1991). · Zbl 0784.05061
[4] M. H. Peel: Specht modules and symmetric groups. J. Alg., 36, 88-97 (1975). · Zbl 0313.20005 · doi:10.1016/0021-8693(75)90158-1
[5] B. Sagan : The Symmetric Groups. Wadsworth and Brooks (1991). · Zbl 0823.05061
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