We give a proof of a conjecture that Kleshchev multipartitions are those partitions which parametrize non-zero simple modules obtained as factor modules of Specht modules by their own radicals.

We introduce a tensor category O+ (resp. O−) of certain modules of ĝl∞ with non-negative (resp. non-positive) integral central charges with the usual tensor product. We also introduce a tensor category (Of , ⊙ ) consisting of certain modules over GL(N) for all N . We show that the tensor categories O± and Of are semisimple abelian and all equivalent to each other. We give a formula to decompose...

2 Highest weight modules 4 2.1 Kac-Moody Lie algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Integral Weyl groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Category of highest weight modules . . . . . . . . . . . . . . . . . . . . . . 9 2.4 Enright functor for non-integral weights . . . . . . . . . . . . . . . . . . . . 11 2.5 Embeddings of Verma m...

A novel module-search algorithm method was used to screen for potential signatures and investigate the molecular mechanisms of inhibiting hepatocellular carcinoma (HCC) growth following treatment with silymarin (SM). The modules algorithm was used to identify the modules via three major steps: i) Seed gene selection; ii) module search by seed expansion and entropy minimization; and iii) module ...

We classify irreducible Whittaker modules for generalized Heisenberg Lie algebra t and irreducible Whittaker modules for Lie algebra t̃ obtained by adjoining m degree derivations d1, d2, . . . , dm to t. Using these results, we construct imaginary Whittaker modules for non-twisted extended affine Lie algebras and prove that the imaginary Whittaker modules of Z-independent level are always irredu...

In this paper, some results on vanishing and non-vanishing of generalized local cohomology modules are presented and some relations between those modules and, Ext and ordinary local cohomology modules are studied. Also, several cofiniteness propositions for generalized local cohomology modules are established which, among other things, provide an alternative answer to a question in [Y2].

let $r$ be a ring and $m$ a right $r$-module with $s=end_r(m)$. a module $m$ is called semi-projective if for any epimorphism $f:mrightarrow n$, where $n$ is a submodule of $m$, and for any homomorphism $g: mrightarrow n$, there exists $h:mrightarrow m$ such that $fh=g$. in this paper, we study sgq-projective and$pi$-semi-projective modules as two generalizations of semi-projective modules. a m...

we consider the class $mathfrak m$ of $bf r$--modules where $bf r$ is an associative ring. let $a$ be a module over a group ring $bf r$$g$, $g$ be a group and let $mathfrak l(g)$ be the set of all proper subgroups of $g$. we suppose that if $h in mathfrak l(g)$ then $a/c_{a}(h)$ belongs to $mathfrak m$. we investigate an $bf r$$g$--module $a$ such that $g not = g'$, $c_{g}(a) = 1$. we stud...