Related papers: Graded induction for Specht modules

Motivated by an equivalence of categories established by Kapranov and Schechtman, we introduce, for each non-negative integer d, the category of connected bialgebras modulo d+1. We show that these categories fit into an inverse system of…

Let $n$ be a positive integer. The main result of this manuscript is a construction of a filtration on the cohomology ring of a regular nilpotent Hessenberg variety in $GL(n,{\mathbb{C}})/B$ such that its associated graded ring has graded…

We consider the principal block of category O and its graded version. On the space of homomorphisms from a Verma module to an indecomposable tilting module we may define natural filtrations following Andersen. The arguments given in this…

We show that graded Hecke algebras are PI algebras if and only if they are finitely generated over their centres if and only if the deformation parameters $t_{i}$ are zero for all $i=1,\ldots,N$. This generalises a result for symplectic…

Results of Vancliff, Van Rompay and Willaert in 1998 prove that point modules over a regular graded Clifford algebra (GCA) are determined by (commutative) quadrics of rank at most two that belong to the quadric system associated to the GCA.…

Let $G,H$ be groups, $\phi: G \rightarrow H$ a group morphism, and $A$ a $G$-graded algebra. The morphism $\phi$ induces an $H$-grading on $A$, and on any $G$-graded $A$-module, which thus becomes an $H$-graded $A$-module. Given an…

We study strongly graded vertex algebras and their strongly graded modules, which are conformal vertex algebras and their modules with a second, compatible grading by an abelian group satisfying certain grading restriction conditions. We…

The Graded Classification Conjecture (GCC) states that the pointed $K_0^{\operatorname{gr}}$-group is a complete invariant of the Leavitt path algebras of finite graphs when these algebras are considered with their natural grading by…

Necessary and sufficient conditions are given for a $G$-graded simple module over a unital associative algebra, graded by an abelian group $G$, to be isomorphic to a loop module of a simple module, as well as for two such loop modules to be…

We introduce the graded bialgebra deformations, which explain Andruskiewitsch-Schneider's liftings method. We also relate this graded bialgebra deformation with the corresponding graded bialgebra cohomology groups, which is the graded…

The restriction of a (dual) Specht module to a smaller symmetric group has a filtration by (dual) Specht modules of this smaller group. In the cellular structure of the group algebra of the symmetric group, the cell modules are exactly the…

We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context.…

In [14] Hemmer conjectures that the module of fixed points for the symmetric group $\Sigma_m$ of a Specht module for $\Sigma_n$ (with $n>m$), over a field of positive characteristic $p$, has a Specht series, when viewed as a…

In this article, we introduce the concepts of graded $s$-prime submodules which is a generalization of graded prime submodules. We study the behavior of this notion with respect to graded homomorphisms, localization of graded modules,…

For a root system of type $B$ we study an algebra similar to a graded Hecke algebra, isomorphic to a subalgebra of the rational Cherednik algebra. We introduce principal series modules over it and prove an irreducibility criterion for these…

This paper describes the module categories for a family of generic Hecke algebras that specialize to the complex reflection groups G(r,1,n) and to the certain endomorphism rings of permutation characters of finite general linear groups. In…

Let h \subset g be an inclusion of Lie algebras with quotient h-module n. There is a natural degree filtration on the h-module U(g)/U(g)h whose associated graded h-module is isomorphic to S(n). We give a necessary and sufficient condition…

Let $\Lambda$ be a $\mathbb{Z}$-graded artin algebra. Two classical results of Gordon and Green state that if $\Lambda$ has only finitely many indecomposable gradable modules, up to isomorphism, then $\Lambda$ has finite representation…

This paper considers Weyl modules for a simple, simply connected algebraic group over an algebraically closed field $k$ of positive characteristic $p\not=2$. The main result proves, if $p\geq 2h-2$ (where $h$ is the Coxeter number) and if…

Using purely combinatorial methods we calculate the first degree cohomology of Specht modules indexed by two part partitions over fields of characteristic $p\ge 3$. These combinatorial methods also allow us to obtain an explicit description…