Elementary divisors of integral Specht modules

1999 ◽  
pp. 165-175
Author(s):  
Andrew Mathas
Keyword(s):  
Specht Modules ◽  
Elementary Divisors

scholarly journals Elementary Divisors of Gram Matrices of Certain Specht Modules

2003 ◽  
Vol 31 (7) ◽  
pp. 3377-3427 ◽  
Author(s):  
M. Künzer ◽  
G. Nebe
Keyword(s):  
Specht Modules ◽  
Elementary Divisors ◽  
Gram Matrices

scholarly journals Elementary divisors of Specht modules

2005 ◽  
Vol 26 (6) ◽  
pp. 943-964 ◽  
Author(s):  
Matthias Künzer ◽  
Andrew Mathas
Keyword(s):  
Specht Modules ◽  
Elementary Divisors

scholarly journals Nonnegative persymmetric matrices with prescribed elementary divisors

2015 ◽  
Vol 483 ◽  
pp. 139-157 ◽  
Author(s):  
Ricardo L. Soto ◽  
Ana I. Julio ◽  
Mario Salas
Keyword(s):  
Elementary Divisors

scholarly journals On the Latent Roots of Certain Matrices

1928 ◽  
Vol 1 (2) ◽  
pp. 135-138 ◽  
Author(s):  
A. C. Aitken
Keyword(s):  
Fundamental Theorem ◽  
Present Note ◽  
Principal Diagonal ◽  
Characteristic Determinant ◽  
Elementary Divisors ◽  
The Right ◽  
Latent Roots

In the present note certain known theorems on the latent roots of matrices are deduced from the fundamental theorem that a matrix A can be expressed in the form PQP-1, where P is non-singular and Q has zero elements everywhere to the left of the principal diagonal, and the latent roots of A in the diagonal. [The presence or absence of non-zero elements to the right of the diagonal is known to depend on the nature of the “elementary divisors” of the “characteristic determinant” of A, but in what follows these will not concern us.]

VI.—On Singular Pencils of Zehfuss, Compound, and Schläflian Matrices

1937 ◽  
Vol 56 ◽  
pp. 50-89 ◽  
Author(s):  
W. Ledermann
Keyword(s):  
Canonical Form ◽  
Direct Product ◽  
Canonical Forms ◽  
Singular Case ◽  
Elementary Divisors ◽  
Compound Matrices ◽  
Matrix Pencils ◽  
The Subject

In this paper the canonical form of matrix pencils will be discussed which are based on a pair of direct product matrices (Zehfuss matrices), compound matrices, or Schläflian matrices derived from given pencils whose canonical forms are known.When all pencils concerned are non-singular (i.e. when their determinants do not vanish identically), the problem is equivalent to finding the elementary divisors of the pencil. This has been solved by Aitken (1935), Littlewood (1935), and Roth (1934). In the singular case, however, the so-called minimal indices or Kronecker Invariants have to be determined in addition to the elementary divisors (Turnbull and Aitken, 1932, chap. ix). The solution of this problem is the subject of the following investigation.

scholarly journals Specht modules for finite reflection groups

1995 ◽  
Vol 37 (3) ◽  
pp. 279-287 ◽  
Author(s):  
S. HalicioǦlu
Keyword(s):  
Present Author ◽  
Symmetric Groups ◽  
Irreducible Representations ◽  
Weyl Groups ◽  
Arbitrary Field ◽  
Young Tableaux ◽  
Reflection Groups ◽  
Specht Modules ◽  
Irreducible Modules ◽  
Original Approach

Over fields of characteristic zero, there are well known constructions of the irreducible representations, due to A. Young, and of irreducible modules, called Specht modules, due to W. Specht, for the symmetric groups Sn which are based on elegant combinatorial concepts connected with Young tableaux etc. (see, e.g. [13]). James [12] extended these ideas to construct irreducible representations and modules over an arbitrary field. Al-Aamily, Morris and Peel [1] showed how this construction could be extended to cover the Weyl groups of type Bn. In [14] Morris described a possible extension of James' work for Weyl groups in general. Later, the present author and Morris [8] gave an alternative generalisation of James' work which is an extended improvement and extension of the original approach suggested by Morris. We now give a possible extension of James' work for finite reflection groups in general.

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