Related papers: Generalized polynomial functors

We give geometric descriptions of the category C_k(n,d) of rational polynomial representations of GL_n over a field k of degree d for d less than or equal to n, the Schur functor and Schur-Weyl duality. The descriptions and proofs use a…

We introduce categories of homogeneous strict polynomial functors, $\Pol^\I_{d,\k}$ and $\Pol^\II_{d,\k}$, defined on vector superspaces over a field $\k$ of characteristic not equal 2. These categories are related to polynomial…

Let $k$ be a commutative $\mathbb{Q}$-algebra. We study families of functors between categories of finitely generated $R$-modules which are defined for all commutative $k$-algebras $R$ simultaneously and are compatible with base changes.…

Polynomial representations of general linear groups and modules over Schur algebras are compared. We work over an arbitrary commutative ring and show that Schur-Weyl duality is the key for an equivalence between both categories.

We study generalizations of Schur functors from categories consisting of flags of vector spaces. We give different descriptions of the category of such functors in terms of representations of certain combinatorial categories and infinite…

We introduce a class of Schur type functions associated with polynomial sequences of binomial type. This can be regarded as a generalization of the ordinary Schur functions and the factorial Schur functions. This generalization satisfies…

The theory of Schur functors provides a powerful and elegant approach to the representation theory of GL_n - at least to the so-called polynomial representations - especially to questions about how the theory varies with n. We develop…

Let $\mathbb{k}$ be a characteristic zero domain. For a locally unital $\mathbb{k}$-superalgebra $A$ with distinguished idempotents $I$and even subalgebra $a \subseteq A_{\bar 0}$, we define and study an associated diagrammatic monoidal…

We use category theory to propose a unified approach to the Schur-Weyl dualities involving the general linear Lie algebras, their polynomial extensions and associated quantum deformations. We define multiplicative sequences of algebras…

We categorify various Fock space representations on the algebra of symmetric functions via the category of polynomial functors. In a prequel, we used polynomial functors to categorify the Fock space representations of type A affine Lie…

We introduce a new functor category: the category $\mathcal{P}_{d,n}$ of strict polynomial functors with bounded by $n$ domain of degree $d$ over a field of characteristic $p>0$. It is equivalent to the category of finite dimensional…

The Schur orthogonality relations are a cornerstone in the representation theory of groups. We utilize a generalization to weak Hopf algebras to provide a new, readily verifiable condition on the skeletal data for deciding whether a given…

We develop a theory of two-parameter quantum polynomial functors. Similar to how (strict) polynomial functors give a new interpretation of polynomial representations of the general linear groups $\operatorname{GL}_n$, the two-parameter…

Let $A$ be a condensable algebra in a modular tensor category $\mathcal{C}$. We define an action of the fusion category $\mathcal{C}_A$ of $A$-modules in $\mathcal{C}$ on the morphism space $\mbox{Hom}_{\mathcal{C}}(x,A)$ for any $x$ in…

Functors involved in Fontaine equivalences decompose as extension of scalars and taking of invariants between full subcategories of modules over a topological ring equipped with semi-linear continuous action of a topological monoid. We give…

Highest weight categories are described in terms of standard objects and recollements of abelian categories, working over an arbitrary commutative base ring. Then the highest weight structure for categories of strict polynomial functors is…

We define an extension of the affine Brauer algebra, the type B/C affine Brauer algebra. This new algebra contains the hyperoctahedral group and it naturally acts on $END_K(X \otimes V^{\otimes k})$ for Orthogonal and Symplectic groups.…

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 describe the class of semi-stable model categories, which generalize the equivalence of finite products and coproducts in abelian and stable model categories, and use this to establish Morita equivalences among categories of functors. We…

Let $A$ be an associative superalgebra over a field of characteristic zero. Let $n \geq d+1$. The main result of the paper establishes an equivalence of categories between supermodules for the wreath product $ S_{d} \wr A$ and an explicitly…