Weyl submodules in restrictions of simple modules

Weyl Submodules in Restrictions of Simple Modules

Let F be an algebraically closed field of characteristic p > 0. Suppose that SLn−1(F) is naturally embedded into SLn(F) (either in the top left corner or in the bottom right corner). We prove that certain Weyl modules over SLn−1(F) can be embedded into the restriction L(ω)↓SL n−1(F), where L(ω) is a simple SLn(F)-module. This allows us to construct new primitive vectors in L(ω)↓SL n−1(F) from a...

Submodules of Specht Modules for Weyl Groups

The construction of all irreducible modules of the symmetric groups over an arbitrary field which reduce to Specht modules in the case of fields of characteristic zero is given by G.D.James. Halıcıoğlu and Morris describe a possible extension of James’ work for Weyl groups in general, where Young tableaux are interpreted in terms of root systems. In this paper we show how to construct submodule...

Submodules of Secondary Modules

Pure Submodules of Multiplication Modules

The purpose of this paper is to investigate pure submodules of multiplication modules. We introduce the concept of idempotent submodule generalizing idempotent ideal. We show that a submodule of a multiplication module with pure annihilator is pure if and only if it is multiplication and idempotent. Various properties and characterizations of pure submodules of multiplication modules are consid...

On the Prime Submodules of Multiplication Modules

By considering the notion of multiplication modules over a commutative ring with identity, first we introduce the notion product of two submodules of such modules. Then we use this notion to characterize the prime submodules of a multiplication module. Finally, we state and prove a version of Nakayama lemma for multiplication modules and find some related basic results. 1. Introduction. Let R b...