Related papers: Good filtrations for generalized Schur algebras

We find the model completion of the theory modules over $A$, where $A$ is a finitely generated commutative algebra over a field $K$. This is done in a context where the field $K$ and the module are represented by sorts in the theory, so…

We give new properties of algebras with finite Gorenstein dimension coinciding with the dominant dimension $\geq 2$, which are called Auslander-Gorenstein algebras in the recent work of Iyama and Solberg, see \cite{IyaSol}. In particular,…

We reformulate the persistent (co)homology of simplicial filtrations, viewed from a more algebraic setting, namely as the (co)homology of a chain complex of graded modules over polynomial ring $K[t]$. We also define persistent (co)homology…

Let G be a locally compact group L^p(G) be the usual L^p-space for 1 =< p =< infty and A(G) be the Fourier algebra of G. Our goal is to study, in a new abstract context, the completely bounded multipliers of A(G), which we denote…

The purpose of this paper is to prove necessary and sufficient criteria for a $GL(m|n)$-supermodule to have a good or Weryl filtration. We also introduce the notion of a Steinberg supermodule analogous to the classical notion of Steinberg…

Let $A$ be an artinian algebra, and let $\mathcal{C}$ be a subcategory of mod$A$ that is closed under extensions. When $\mathcal{C}$ is closed under kernels of epimorphisms (or closed under cokernels of monomorphisms), we describe the…

In this paper the authors investigate the $q$-Schur algebras of type B that were constructed earlier using coideal subalgebras for the quantum group of type A. The authors present a coordinate algebra type construction that allows us to…

We study canonical filtrations of finite-dimensional associative algebras and Lie algebras. These filtrations are defined via optimal destabilizing one-parameter subgroups in the sense of geometric invariant theory (GIT), and appear to be a…

We introduce super-analogues of the Schur functors defined by Akin, Buchsbaum and Weyman. These {\em Schur superfunctors} may be viewed as characteristic-free analogues of the finite dimensional atypical irreducible modules over the Lie…

We introduce the notion of homological systems $\Theta$ for triangulated categories. Homological systems generalize, on one hand, the notion of stratifying systems in module categories, and on the other hand, the notion of exceptional…

In this paper, we construct a large class of new simple modules over the twisted $N=2$ superconformal algebra. These new simple modules are restricted modules based on the simple modules over certain finite-dimensional solvable Lie…

Finite-dimensional Reedy algebras form a ring-theoretic analogue of Reedy categories and were recently proved to be quasi-hereditary. We identify Reedy algebras with quasi-hereditary algebras admitting a triangular (or…

We introduce the notion of quantum Schur (or $q$-Schur) superalgebras. These algebras share certain nice properties with $q$-Schur algebras such as base change property, existence of canonical $\mathbb Z[v,v^{-1}]$-bases, and the duality…

We give an algebraic construction of standard modules (infinite dimensional modules categorifying the PBW basis of the underlying quantized enveloping algebra) for Khovanov-Lauda-Rouquier algebras in all finite types. This allows us to…

Green and Schroll give an easy criterion for a monomial algebra $A$ to be quasi-hereditary with respect to some partial order $\leq_A$. A natural follow-up question is under which conditions a monomial quasi-hereditary algebra $(A, \leq_A)$…

We reprove the main result of our joint work [arXiv:0706.0604] with Srinivas, concerning finite Schur filtration dimension, but now with the base field replaced by a commutative noetherian ring k. This leads to finiteness results for the…

We show that canonical bases in $\dot{U}(\mathfrak{sl}_n)$ and the Schur algebra are compatible; in fact we extend this result to $p$-canonical bases. This follows immediately from a fullness result from a functor categorifying this map. In…

We define and study generalized nil-Coxeter algebras associated to Coxeter groups. Motivated by a question of Coxeter (1957), we construct the first examples of such finite-dimensional algebras that are not the 'usual' nil-Coxeter algebras:…

We study the Hecke algebra modules arising from theta correspondence between certain Harish-Chandra series for type I dual pairs over finite fields. For the product of the pair of Hecke algebras under consideration, we show that there is a…

We treat the $\tau$-tilting finiteness of those minimal representation-infinite (min-rep-infinite) algebras which are non-distributive. Building upon the new results of Bongartz, we fully determine which algebras in this family are…