相关论文: Tensor product varieties and crystals. GL case

We define and study a certain relative tensor product of subfactors over a modular tensor category. This gives a relative tensor product of two completely rational heterotic full local conformal nets with trivial superselection structures…

We establish a tensor product theorem for slope semistable parabolic $\lambda$-connections over smooth projective varieties in arbitrary characteristic.

Matrix product states play an important role in quantum information theory to represent states of many-body systems. They can be seen as low-dimensional subvarieties of a high-dimensional tensor space. In these notes, we consider two…

Determining the Jordan canonical form of the tensor product of Jordan blocks has many applications including to the representation theory of algebraic groups, and to tilting modules. Although there are several algorithms for computing this…

It is well known that the cohomology of a tensor product is essentially the tensor product of the cohomologies. We look at twisted tensor products, and investigate to which extend this is still true. We give an explicit description of the…

We prove a noncommutative Bader-Shalom factor theorem for lattices with dense projections in product groups. As an application of this result and our previous works, we obtain a noncommutative Margulis factor theorem for all irreducible…

We describe, in terms of generators and relations, the reduction algebra, related to the diagonal embedding of the Lie algebra $\gl_n$ into $\gl_n\oplus\gl_n$. Its representation theory is related to the theory of decompositions of tensor…

In the stable general linear group over an arbitrary field, we prove that every element with determinant $\pm 1$ is the product of three involutions, and of no less in general. We also obtain several results of the same flavor, with…

The group invariance of entanglement is obtained within a very general and simple setup of the latter, given by a recently introduced considerably extended concept of tensor products. This general approach to entanglement - unlike the usual…

We study how tensor products of representations decompose when restricted from a compact Lie algebra to one of its subalgebras. In particular, we are interested in tensor squares which are tensor products of a representation with itself. We…

By the unfolding method, Rankin-Selberg L-functions for ${\rm GL}(n)\times{\rm GL}(m)$ can be expressed in terms of period integrals. These period integrals actually define invariant forms on tensor products of the relevant automorphic…

Let $\mathbf{G}$ be either a simple linear algebraic group over an algebraically closed field of positive characteristic or a quantum group at a root of unity. We define new classes of indecomposable $\mathbf{G}$-modules, which we call…

Let G be a connected semisimple complex algebraic group and let P be a parabolic subgroup. In this paper we define a new (commutative and associative) product on the cohomology of the homogenous spaces G/P and use this to give a more…

The necessary and sufficient Horn inequalities which determine the non-vanishing Littlewood-Richardson coefficients in the cohomology of a Grassmannian are recursive in that they are naturally indexed by non-vanishing Littlewood-Richardson…

Tensor products of ultrafilters have special combinatorial features closely related to Ramsey's Theorem, making them useful tools in applications. Here we first review their fundamental properties and isolate some new ones, including a…

We give a new construction of tensor product gamma factors for a pair of irreducible representations of $\operatorname{GL}_c\left(\mathbb{F}_q\right)$ and $\operatorname{GL}_k\left(\mathbb{F}_q\right)$. This construction is a finite field…

We make progress towards understanding the structure of Littlewood-Richardson coefficients $g_{\lambda,\mu}^{\nu}$ for products of Jack symmetric functions. Building on recent results of the second author, we are able to prove new cases of…

In this paper we establish a Steinberg-Lusztig tensor product theorem for abstract Fock space. This is a generalization of the type A result of Leclerc-Thibon and a Grothendieck group version of the Steinberg-Lusztig tensor product theorem…

In a categorification of tensor products of fundamental representations of quantum sl(k) via highest weight categories, the indecomposable tilting modules descend to the canonical basis. Since projective functors map tilting modules to…

We study a particular category ${\cal{C}}$ of $\gl_{\infty}$-modules and a subcategory ${\cal{C}}_{int}$ of integrable $\gl_{\infty}$-modules. As the main results, we classify the irreducible modules in these two categories and we show that…