Related papers: On the tensor product of linear sites and Grothend…

As part of the study of correspondence functors, the present paper investigates their tensor product and proves some of its main properties. In particular, the correspondence functor associated to a finite lattice has the structure of a…

The category of $C^*$-algebras is blessed with many different tensor products. In contrast, virtually the only tensor product ever used in the category of von Neumann algebras is the normal spatial tensor product. We propose a definition of…

In this paper we study modular tensor categories (braided rigid balanced tensor categories with additional finiteness and non-degeneracy conditions), in particular, representations of quantum groups at roots of unity. We show that the…

In this note, inspired by the proof of the Kirillov-Reshetikhin conjecture, we consider tensor products of Kirillov-Reshetikhin modules of a fixed node and various level. We fix a positive integer and attach to each of its partitions such a…

We develop a Harder-Narasimhan theory for Kisin modules generalizing a similar theory for finite flat group schemes due to Fargues. We prove the tensor product theorem, i.e., that the tensor product of semi-stable objects is again…

This work concerns representations of a finite flat group scheme $G$, defined over a noetherian commutative ring $R$. The focus is on lattices, namely, finitely generated $G$-modules that are projective as $R$-modules, and on the full…

We present a program that allows for the computation of tensor products of irreducible representations of Lie algebras A-G based on the explicit construction of weight states. This straightforward approach (which is slower and more…

We state a conjecture that relates the derived category of smooth representations of a p-adic split reductive group with the derived category of (quasi-)coherent sheaves on a stack of L-parameters. We investigate the conjecture in the case…

A finite tensor category is called pointed if all its simple objects are invertible. We find necessary and sufficient conditions for two pointed semisimple categories to be dual to each other with respect to a module category. Whenever the…

We give an explicit construction of the dependent product in an elementary topos, and a site-theoretic description for it in the case of a Grothendieck topos.

Consider a Grothendieck category $\mathcal{G}$ along with a choice of generator $G$, or equivalently a generating set $\{G_i\}$. We introduce the derived category $\mathcal{D}(G)$, which kills all $G$-acyclic complexes, by putting a…

We develop some foundations of commutative algebra, with a view towards algebraic geometry, in symmetric tensor categories. Most results establish analogues of classical theorems, in tensor categories which admit a tensor functor to some…

The category of modules over a string algebra is equipped with a tensor product defined point-wise and arrow-wise in terms of the underlying quiver. In the present article we investigate how this tensor product interacts with the…

The depth of tensor product of modules over a Gorenstein local ring is studied. For finitely generated modules M and N over a Gorenstein local ring R, under some assumptions on the vanishing of finite number of Tate and relative homology…

We prove an explicit formula for the tensor product with itself of an irreducible complex representation of the symmetric group defined by a rectangle of height two. We also describe part of the decomposition for the tensor product of…

Let $V$ be a M\"{o}bius vertex algebra and $G$ an abelian group of automorphisms of $V$. We construct $P(z)$-tensor product bifunctors for the category of $C_{n}$-cofinite grading-restricted generalized $g$-twisted $V$-modules (without…

We provide a classification of multiplicity-free inner tensor products of irreducible characters of symmetric groups, thus confirming a conjecture of Bessenrodt. Concurrently, we classify all multiplicity-free inner tensor products of skew…

We give a full classification of all braided semisimple tensor categories whose Grothendieck semiring is the one of Rep(O(\infty) (formally), Rep(O(N), Rep(Sp(N) or of one of its associated fusion categories. If the braiding is not…

Categorical bundles provide a natural framework for gauge theories involving multiple gauge groups. Unlike the case of traditional bundles there are distinct notions of triviality, and hence also of local triviality, for categorical…

Continuous frames and tensor products are important topics in theoretical physics. This paper combines those concepts. We derive fundamental properties of continuous frames for tensor product of Hilbert spaces. This includes, for example,…