Related papers: Webs of type Q

We consider the monoidal subcategory of finite dimensional representations of $U_q(\mathfrak{gl}(1|1))$ generated by the vector representation, and we provide a diagram calculus for the intertwining operators, which allows to compute…

As a natural generalization quantum Schur algebras associated with the Hecke algebra of the symmetric group, we introduce the quantum Schur superalgebra of type Q associated with the Hecke-Clifford superalgebra, which, by definition, is the…

We endow categories of non-symmetric operads with natural model structures. We work with no restriction on our operads and only assume the usual hypotheses for model categories with a symmetric monoidal structure. We also study categories…

We review the q-deformed spin network approach to Topological Quantum Field Theory and apply these methods to produce unitary representations of the braid groups that are dense in the unitary groups. Our methods are rooted in the bracket…

In this expository paper, we discuss and compare the notions of braided and coboundary monoidal categories. Coboundary monoidal categories are analogues of braided monoidal categories in which the role of the braid group is replaced by the…

This paper develops a theory of monoidal categories relative to a braided monoidal category, called augmented monoidal categories. For such categories, balanced bimodules are defined using the formalism of balanced functors. The two main…

A linking pairing is a symetric bilinear pairing lambda: GxG --> Q/Z on a finite abelian group. The set of isomorphism classes of linking pairings is a non-cancellative monoid E under orthogonal sum, which is infinitely generated and…

The irreducible representations of symmetric groups can be realized as certain graded pieces of invariant rings, equivalently as global sections of line bundles on partial flag varieties. There are various ways to choose useful bases of…

Let $ Aut_{mHH}(H)$ denote a set of all automorphisms of a monoidal Hopf algebra $H$ with bijective antipode in the sense of Caenepeel S. and Goyvaerts I. (Commun. Algebra 39, 2216-2240, 2011) and let $G$ be a crossed product group $…

We establish a Quillen model category structure on the category of symmetric simplicial multicategories. This model structure extends the model structure on simplicial categories due to J. Bergner.

This article gives a solid theoretical grounding to the observation that cubical structures arise naturally when working with parametricity. We claim that cubical models are cofreely parametric. We use categories, lex categories or clans as…

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 $\mathcal{S}$ be a small category admitting binary products. We show that the whole theory of monoidal $\mathcal{S}$-fibered categories, which is customarily formulated in terms of the usual internal tensor product, can be rephrased…

We develop algebraic models of simple type theories, laying out a framework that extends universal algebra to incorporate both algebraic sorting and variable binding. Examples of simple type theories include the unityped and simply-typed…

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.

Let V be the representation of the quantised enveloping algebra of a general linear group which is the q-analogue of the vector representation. In this paper we construct a basis of the representations obtained by tensoring copies of V and…

In this short note we study Lie algebras in the framework of symmetric monoidal categories. After a brief review of the existing work in this field and a presentation of earlier studied and new examples, we examine which functors preserve…

We show that every unitarizable fusion category, and more generally every semisimple C*-tensor category, admits a unique unitary structure. Our proof is based on a categorified polar decomposition theorem for monoidal equivalences between…

We classify all simple supermodules over the queer Lie superalgebra $\mathfrak{q}_{2}$ up to classification of equivalence classes of irreducible elements in a certain Euclidean ring.

Webs are planar graphs with boundary that describe morphisms in a diagrammatic representation category for $\mathfrak{sl}_k$. They are studied extensively by knot theorists because braiding maps provide a categorical way to express link…