Top-down design methodology is one of the widely used approaches to the design of complex concurrent systems. In this approach, the speciication of a system is decomposed into a set of submodules whose concurrent behavior is equivalent to that of the system speciication. The following problem is of particular importance when using this methodology: given the speciication of a system and some of...

We consider the problem of decomposing tensor powers of the fundamental level 1 highest weight representation V of the affine Kac-Moody algebra g(E9). We describe an elementary algorithm for determining the decomposition of the submodule of V ⊗n whose irreducible direct summands have highest weights which are maximal with respect to the null-root. This decomposition is based on Littelmann’s pat...

We consider the problem of decomposing tensor powers of the fundamental level 1 highest weight representation V of the affine Kac-Moody algebra g(E9). We describe an elementary algorithm for determining the decomposition of the submodule of V ⊗n whose irreducible direct summands have highest weights which are maximal with respect to the null-root. This decomposition is based on Littelmann’s pat...

Corollary 1.2 Let G be an almost simple classical group with natural module V of dimension n. If G is linear, assume that G does not contain a graph automorphism. Let 2 ≤ k < n − 1, and let K be the stabilizer of a nondegenerate or totally singular k-space of V . Let P be the stabilizer of a singular 1-space of V . Then the permutation module 1P is a submodule of 1 G K unless one of the followi...

Mediator is a modular multiprotein complex required for regulated transcription by RNA polymerase (Pol) II. Here, we show that the middle module of the Mediator core contains a submodule of unique structure and function that comprises the N-terminal part of subunit Med7 (Med7N) and the highly conserved subunit Med31 (Soh1). The Med7N/31 submodule shows a conserved novel fold, with two proline-r...

In a finite-dimensional vector space, every subspace is finite-dimensional and the dimension of a subspace is at most the dimension of the whole space. Unfortunately, the naive analogue of this for modules and submodules is wrong: (1) A submodule of a finitely generated module need not be finitely generated. (2) Even if a submodule of a finitely generated module is finitely generated, the minim...

12.1.2. Let M be a module over the integral domain R. (a) Assume that M has rank n and that x1, . . . , xn is any maximal set of linearly independent elements of M . Prove that N is isomorphic to Rn and that the quotient M/N is a torsion Rmodule. (b) Prove conversely that if M contains a submodule N that is free of rank n (i.e., N › Rn) such that the quotient M/N is a torsion R-module then M ha...

We consider the problem of decomposing tensor powers of the fundamental level 1 highest weight representation V of the affine Kac-Moody algebra g(E9). We describe an elementary algorithm for determining the decomposition of the submodule of V ⊗n whose irreducible direct summands have highest weights which are maximal with respect to the null-root. This decomposition is based on Littelmann’s pat...

in this paper we introduce the notions of g∗l-module and g∗l-module whichare two proper generalizations of δ-lifting modules. we give some characteriza tions and properties of these modules. we show that a g∗l-module decomposesinto a semisimple submodule m1 and a submodule m2 of m such that every non-zero submodule of m2 contains a non-zero δ-cosingular submodule.

Definition 2.1. Let R be a ring. A left R-module is an abelian group (M,+) together with an R-action · : R ×M → M which satisfies M1 1 ·m = m for all m ∈ M; M2 r(s ·m) = (r s) ·m for all r, s ∈ R and m ∈ M; M3 r · (m + n) = (r ·m) + (s · n) A submodule N of M is a subset which is closed under + and satisfies r · n ∈ N for all r ∈ R and n ∈ N. A right R-module is defined similarly, but modules w...