相关论文: Submodules of Specht Modules for Weyl Groups

Over fields of characteristic zero, there are well known construction of the irreducible representations and of irreducible modules, called Specht modules for the symmetric groups $S_{n}$ which are based on elegant combinatorial concepts…

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 $S_{n}$ which are based…

For any prime p, we construct, and simultaneously count, all of the complex Specht modules in a given p-block of the symmetric group which remain irreducible when reduced modulo p. We call the Specht modules with this property p-irreducible…

In this paper we study the vertices of indecomposable Specht modules for symmetric groups. For any given indecomposable non-projective Specht module, the main theorem of the article describes a family of p-subgroups contained in its vertex.…

We construct the irreducible unipotent modules of the finite general linear groups using tableaux. Our construction is analogous to that of James (1976) for the symmetric groups, answering an open question as to whether such a construction…

By a result of Hemmer, every simple Specht module of a finite symmetric group over a field of odd characteristic is a signed Young module. While Specht modules are parametrized by partitions, indecomposable signed Young modules are…

This paper studies the vertices, in the sense defined by J. A. Green, of Specht modules for symmetric groups. The main theorem gives, for each indecomposable non-projective Specht module, a large subgroup contained in one of its vertices. A…

In the representation theory of split reductive algebraic groups, it is well known that every Weyl module with minuscule highest weight is irreducible over every field. Also, the adjoint representation of $E_8$ is also irreducible over…

We compute explicitly the submodule structure of the Young modules for symmetric groups $S_n$ over fields of characteristic 2, when $n \le 7$. We use this information to compute the submodule structure of indecomposable projectives for the…

We realize the integral Specht modules for the symmetric group $S_n$ as induced modules from the subalgebra of the group algebra generated by the Jucys-Murphy elements. We deduce from this that the simple modules for $FS_n$ are generated by…

We construct a new family of homomorphisms from Specht modules into Foulkes modules for the symmetric group. These homomorphisms are used to give a combinatorial description of the minimal partitions (in the dominance order) which label…

The authors proved that a Weyl module for a simple algebraic group is irreducible over every field if and only if the module is isomorphic to the adjoint representation for $E_{8}$ or its highest weight is minuscule. In this paper, we prove…

Recently Donkin defined signed Young modules as a simultaneous generalization of Young and twisted Young modules for the symmetric group. We show that in odd characteristic, if a Specht module $S^\lambda$ is irreducible, then $S^\lambda$ is…

The submodule structure of general Specht modules in prime characteristic is a difficult open problem. Kleshchev and Sheth [Journal of Algebra, 221(2), pp.705-722] gave a combinatorial description of the submodule structure of Specht…

Describing the decomposition of Foulkes module $F_b^a$ into irreducible Specht modules is an open problem for $a,b > 3$. In this article we provide a new approach for the Generalized Foulkes module $F_{\nu}^a$ (with arbitrary partition…

The Springer correspondence makes a link between the characters of a Weyl group and the geometry of the nilpotent cone of the corresponding semisimple Lie algebra. In this article, we consider a modular version of the theory, and show that…

We determine the characters of the simple composition factors and the submodule lattices of certain Weyl modules for classical groups. The results have several applications. The simple modules arise in the study of incidence systems in…

For an irreducible module $P$ over the Weyl algebra $\mathcal{K}_n^+$ (resp. $\mathcal{K}_n$) and an irreducible module $M$ over the general liner Lie algebra $\mathfrak{gl}_n$, using Shen's monomorphism, we make $P\otimes M$ into a module…

During the 2004-2005 academic year the VIGRE algebra research group at the University of Georgia computed the complexities of certain Specht modules S^\lambda for the symmetric group, using the computer algebra program Magma. The complexity…

James' submodule theorem is a fundamental result in the representation theory of the symmetric groups and the finite general linear groups. In this note we consider a version of that theorem for a general finite group with a split…