Related papers: Webs and $q$-Howe dualities in types $\mathbf{B}\m…

For any Levi subalgebra of the form $\mathfrak{l}=\mathfrak{gl}_{l_{1}}\oplus\dots\oplus\mathfrak{gl}_{l_{d}}\subseteq\mathfrak{gl}_{n}$ we construct a quotient of the category of annular quantum $\mathfrak{gl}_{n}$ webs that is equivalent…

We establish classical and categorical Howe dualities between the Lie superalgebras $\mathfrak{p}(m)$ and $\mathfrak{p}(n)$, for $m,n \geq 1$. We also describe a presentation via generators and relations as well as a Kostant…

Webs are combinatorial diagrams used to encode homomorphisms between representations of Lie (super)algebras and related objects. This paper extends the theory of webs to the quantum group of type Q. We define a monoidal supercategory of…

We give a diagrammatic presentation in terms of generators mod relations of the representation category of $U_q(\mathfrak{sl}_n)$. More precisely, we produce all the relations among $\rm{SL}_n$-webs, thus describing the full subcategory…

We prove a nonsemisimple quantum version of Howe's duality with the rank 2n symplectic and the rank 2 special linear group acting on the exterior algebra of type C. We also discuss the first steps towards the symplectic analog of harmonic…

We give a $q$-analogue of Howe duality associated to a pair $(\mf{g},G)$, where $\mf{g}$ is an orthosymplectic Lie superalgebra and $G=O_\ell, Sp_{2\ell}$. We define explicitly {commuting actions} of a quantized enveloping algebra of…

In this paper we use colored sl(N)-matrix factorizations, due to Wu and Y.Y., in order to categorify part of the quantum skew Howe duality defined by Cautis, Kamnitzer and Morrison. In particular, we define web categories and…

We use super $q$-Howe duality to provide diagrammatic presentations of an idempotented form of the Hecke algebra and of categories of $\mathfrak{gl}_N$-modules (and, more generally, $\mathfrak{gl}_{N|M}$-modules) whose objects are tensor…

We define a new $q$-deformation of Brauer's centralizer algebra which contains Hecke algebras of type $A$ as unital subalgebras. We determine its generic structure as well as the structure of certain semisimple quotients. This is expected…

We establish a quantum analogue of the classical metaplectic Howe duality involving the pair of Lie algebras $(\mathfrak{sp}_{2n},\mathfrak{sl}_2)$ in the case when $n=1$. Our results yield commuting representations of the pair of…

We introduce web supercategories of type Q. We describe the structure of these categories and show they have a symmetric braiding. The main result of the paper shows these diagrammatically defined monoidal supercategories provide…

We develop a geometric approach toward an interplay between a pair of quantum Schur algebras of arbitrary finite type. Then by Beilinson-Lusztig-MacPherson's stabilization procedure in the setting of partial flag varieties of type A (resp.…

We give a new combinatorial interpretation of Howe dual pairs of the form $(\g,{\rm Sp}_{2\ell})$, where $\g$ is a Lie (super)algebra of classical type. This is done by establishing a symplectic analogue of the RSK algorithm associated to…

Howe's duality is considered from a unifying point of view based on Lie superalgebras. New examples are offered. In particular, we construct several simplest spinor-oscillator representations and compute their highest weights for the…

We define a diagrammatic category that is equivalent to tilting representations for the orthogonal group. Our construction works in characteristic not equal to two. We also describe the semisimplification of this category.

We define a $\mathbb{C}(q)$-linear pivotal category $\mathbf{Web}(\mathfrak{sp}_{2n})$ and prove that it is equivalent to the full subcategory of finite-dimensional representations of $U_q(\mathfrak{sp}_{2n})$ tensor-generated by the…

We describe how certain cyclotomic Nazarov-Wenzl algebras occur as endomorphism rings of projective modules in a parabolic version of BGG category O of type $D$. Furthermore we study a family of subalgebras of these endomorphism rings which…

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 introduce a new diagrammatic $\Bbbk$-linear monoidal supercategory $QWeb^\bullet$, the affine web supercategory of type $Q$, where $\Bbbk$ is a commutative ring of characteristic not two. This category is the affinization of the web…

This note is a sequel to Shu-Xue-Yao's paper \cite{BYY} where the author studied the so-called enhanced groups and related dualities for type $A$. In this note, we continue to investigate the enhanced dualities for classical groups of type…