Related papers: Highest weight categories and strict polynomial fu…
Highest weight categories arising in Lie theory are known to be associated with finite dimensional quasi-hereditary algebras such as Schur algebras or blocks of category $\mathcal O$. An analogue of the PBW theorem will be shown to hold for…
Highest weight categories are an abstraction of the representation theory of semisimple Lie algebras introduced by Cline, Parshall and Scott in the late 1980s. There are by now many characterisations of when an abelian category is highest…
We develop axiomatics of highest weight categories and quasi-hereditary algebras in order to incorporate two semi-infinite situations which are in Ringel duality with each other; the underlying posets are either upper finite or lower…
In this paper we present criteria in terms of dual pairs of exceptional sequences for an abelian category to be highest weight. The criteria are applied in three situations of geometric origin. We give new proofs for the facts that the…
We provide several equivalent descriptions of a highest weight category using recollements of abelian categories. Also, we explain the connection between sequences of standard and exceptional objects.
We study linear versions of Reedy categories in relation with finite dimensional algebras and abelian model structures. We prove that, for a linear Reedy category $\mathcal{C}$ over a field, the category of left $\mathcal{C}$--modules…
We prove that the category of finitely generated graded modules over the quiver Hecke algebra of arbitrary type admits numerous stratifications in the sense of Kleshchev. A direct consequence is that the full subcategory corresponding to…
Work of Grantcharov et al. develops a theory of abstract crystals for the queer Lie superalgebra $\mathfrak{q}_n$. Such $\mathfrak{q}_n$-crystals form a monoidal category in which the connected normal objects have unique highest weight…
We show that the category of graded modules over a finite-dimensional graded algebra admitting a triangular decomposition can be endowed with the structure of a highest weight category. When the algebra is self-injective, we show…
This is the second of a series of four articles studying various generalisations of Khovanov's diagram algebra. In this article we develop the general theory of Khovanov's diagrammatically defined "projective functors" in our setting. As an…
This paper is based on the observation that dimension of weight spaces of multi-variable Weyl modules depends polynomially on the highest weight (Conjecture 1). We support this conjecture by various explicit answers for up to three variable…
In this paper, we introduce a family of symmetric polynomials by specializing the factorial Schur polynomials. These polynomials represent the weighted Schubert classes of the cohomology of the weighted Grassmannian introduced by…
We define analogues of Verma modules for finite W-algebras. By the usual ideas of highest weight theory, this is a first step towards the classification of finite dimensional irreducible modules. Motivated by known results in type A, we…
In [19], Zheng studied the bounded derived categories of constructible $\bar{\mathbb{Q}}_l$-sheaves on some algebraic stacks consisting of the representations of a enlarged quiver and categorified the integrable highest weight modules of…
We define a family of universal finite-dimensional highest weight modules for affine Lie algebras, we call these Weyl modules. We conjecture that these are the classical limits of the irreducible finite--dimensional representations of the…
We define Weyl functors, global modules for equivariant map Lie superalgebras $(\g \otimes A)^{\Gamma}$, where $\g$ is basic classical $\mathbb{C}$- Lie superalgebra and $A$ is an associative commutative unital $\mathbb{C}$-algebra. Under…
We develop a new approach to highest weight categories $\cal{C}$ with good (and cogood) posets of weights via pseudocompact algebras by introducing ascending (and descending) quasi-hereditary pseudocompact algebras. For $\cal{C}$ admitting…
We study highest weight vectors for symmetric and alternating spaces of tensors, whose dimensions are given by generalized Kronecker coefficients. We describe the algebraic relations for classical constructions of corresponding spanning…
This paper continues the study of highest weight categorical sl_2-actions started in part I. We start by refining the definition given there and showing that all examples considered in part I are also highest weight categorifications in the…
We study the homological algebra in the category $\mathcal{P}_p$ of strict polynomial functors of degree $p$ over a field of positive characteristic $p$. We determine the decomposition matrix of our category and we calculate the Ext-groups…