zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
An explicit model for the complex representations of S n . (English) Zbl 0695.20008

The authors provide the following elegant construction of the model character (the sum of all the irreducibles) for the symmetric group, in terms of plethysms and using the Littlewood-Richardson rule:

αn [α]= 0kn/2 ([2][k])[1 n-2k ]·

Reviewer: A.Kerber

20C30Representations of finite symmetric groups
[1]G. D.James and A.Kerber, The representation theory of the symmetric group. Encyclopedia Math. Appl.16, Reading, Mass. 1981.
[2]A. A. Klja?ko, Models for the complex representations of the groupsGL(n,q) and Wey1 groups. Soviet Math. Dokl.24, 496-499 (1981).
[3]J. Saxl, On multiplicity-free permutation representations. In: Finite geometries and designs, London Math. Soc. Lecture Notes49, 337-353 (1981).
[4]J. G.Thompson, Fixed point free involutions and finite projective planes. In: Finite simple groups II (ed. M. J. Collins), New York-London 1980.
[5]R. M. Thrall, On symmetrized Kronecker powers and the structure of the free Lie ring. Amer. J. Math.64, 371-388 (1942). · Zbl 0061.04201 · doi:10.2307/2371691