Related papers: Affine and cyclotomic webs

We define the affinization of an arbitrary monoidal category $\mathcal{C}$, corresponding to the category of $\mathcal{C}$-diagrams on the cylinder. We also give an alternative characterization in terms of adjoining dot generators to…

This paper describes a polynomial invariant of virtual knots that is defined in terms of an integer labeling of the virtual knot diagram. This labeling is seen to derive from an essentially unique structure of affine flat biquandle for flat…

This paper introduces monoidal (super)categories resembling the Brauer category. For all categories, we can construct bases of the hom-spaces using Brauer diagrams. These categories include the Brauer category, its deformation the…

Much of modern Schubert calculus is centered on Schubert varieties in the complete flag variety and on their classes in its integral cohomology ring. Under the Borel isomorphism, these classes are represented by distinguished polynomials…

This is an expended and revised version of the preprint "Schematization of homotopy types". The purpose of this work is to introduce a notion of \emph{affine stacks}, which is a homotopy version of the notion of affine schemes, and to give…

A functor of sets $\mathbb X$ over the category of $K$-commutative algebras is said to be an affine functor if its functor of functions, $\mathbb A_{\mathbb X}$, is reflexive and $\mathbb X=\Spec \mathbb A_{\mathbb X}$. We prove that affine…

We introduce the notion of meromorphic tensor category and illustrate it in several examples. They include representations of quantum affine algebras, chiral algebras of Beilinson and Drinfeld, G-vertex algebras of Borcherds, and…

The quantum groups of finite and affine type $A$ admit geometric realizations in terms of partial flag varieties of finite and affine type $A$. Recently, the quantum group associated to partial flag varieties of finite type $B/C$ is shown…

Let $U_q'(\mathfrak{g})$ be a quantum affine algebra of arbitrary type and let $\mathcal{C}_{\mathfrak{g}}$ be Hernandez-Leclerc's category. We can associate the quantum affine Schur-Weyl duality functor $F_D$ to a duality datum $D$ in…

We prove that every smooth affine variety of dimension $d$ embeds into every simple algebraic group of dimension at least $2d+2$. We do this by establishing the existence of embeddings of smooth affine varieties into the total space of…

Koenig and Xi introduced {\em affine cellular algebras}. Kleshchev and Loubert showed that an important class of {\em infinite dimensional} algebras, the KLR algebras $R(\Gamma)$ of finite Lie type $\Gamma$, are (graded) affine cellular; in…

This paper is meant to be a short review and summary of recent results on the structure of finite and affine classical W-algebras, and the application of the latter to the theory of generalized Drinfeld-Sokolov hierarchies.

Sherman-Zelevinsky and Cerulli constructed canonically positive bases in cluster algebras associated to affine quivers having at most three vertices. Both constructions involve cluster monomials and normalized Chebyshev polynomials of the…

We introduce the notion of standard multipartitions and establish a one-to-one correspondence between standard multipartitions and irreducible representations with integral weights for the affine Hecke algebra of type A with a parameter q…

In arXiv:math/0606241v2 M. Kontsevich and Y. Soibelman argue that the category of noncommutative (thin) schemes is equivalent to the category of coalgebras. We propose that under this correspondence the affine scheme of a k-algebra A is the…

We construct a finitary additive 2-category whose Grothendieck ring is isomorphic to the semigroup algebra of the monoid of order-decreasing and order-preserving transformations of a finite chain.

We give a new construction of the algebraic $K$-theory of small permutative categories that preserves multiplicative structure, and therefore allows us to give a unified treatment of rings, modules, and algebras in both the input and…

Let A be a finite dimensional, unital, and associative algebra which is endowed with a non-degenerate and invariant inner product. We give an explicit description of an action of cyclic Sullivan chord diagrams on the normalized Hochschild…

We show that the principal types of the closed terms of the affine fragment of $\lambda$-calculus, with respect to a simple type discipline, are structurally isomorphic to their interpretations, as partial involutions, in a natural Geometry…

Let $G$ be a semisimple simply-connected algebraic group over an algebraically closed field of characteristic zero. We prove that the affine Hecke category associated to the loop group of $G$ is equivalent to the colimit, evaluated in the…