On the representations of the full matrix semigroup on homogeneous polynomials. II
type: Item
instance of: scholarly article
title: On the representations of the full matrix semigroup on homogeneous polynomials. II
zbMATH Open document ID: 0588.20040
DOI: 10.1016/0021-8693(86)90142-0
author: Leonid Krop
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: This paper is a continuation of the author's paper on the same subject [cf. the preceding review]. With the same notations as there the author describes the structure of W in the singular case: The author proves: (1) For every partition \(\lambda =(r,q)\), \(q\leq r\leq p-2\) the module \(S^{\lambda}\uparrow {\mathcal S}_{| \lambda | +1}\) is a distributive \({\mathcal S}_ n\)-module. (2) \(W^{(d)}\) is a D-module over \(M_ n\), \(n\geq d\) if and only if d is as follows: (i) If \(p>5\), then \(d<p^ 2\) and when d is written to the base p, \(d=a+bp\) we have (a) \(b\leq a+4\) and (b) \(a+b\leq p+1\). (ii) If \(p=5\), then add \(d=28\) to the condition on d given in (i). (iii) If \(p=3\), then add \(d=10,11\) to the conditions given in (i). (iv) If \(p=2\), then \(d<6\).
Mathematics Subject Classification ID: 20M30
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 20H20
Mathematics Subject Classification ID: 15A30
zbMATH DE Number: 3944156
zbMATH Keywords: composition factors
zbMATH Keywords: singular
zbMATH Keywords: distributivity
zbMATH Keywords: semigroup of matrices
zbMATH Keywords: permutation module
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90142-0
OpenAlex ID: W4205803349
cites work: The representation theory of the symmetric groups
cites work: The module orthogonal to the Specht module
description: scientific article; zbMATH DE number 3944156