Tensor product decompositions and rigidity of full factors

Revisiting Brauer’s formula for tensor product decompositions

The notation used here will be explained below. A familiar (though oversimplified) example is given for the Lie algebra sl2(C) by the Clebsch– Gordan formula; as in [2, Exer. 22.7]. In 1937 Richard Brauer published a short note giving a general formula of this sort. It still serves as the starting point for some computer methods, even though it usually involves a large number of cancellations. ...

Tensor Decompositions with Banded Matrix Factors

The computation of themodel parameters of a Canonical Polyadic Decomposition (CPD), also known as the parallel factor (PARAFAC) or canonical decomposition (CANDECOMP) or CP decomposition, is typically done by resorting to iterative algorithms, e.g. either iterative alternating least squares type or descent methods. In many practical problems involving tensor decompositions such as signal proces...

Tensor Product Decompositions and Open Orbits in Multiple Flag Varieties

For a connected semisimple algebraic group G, we consider some special infinite series of tensor products of simple G-modules whose G-fixed point spaces are at most one-dimensional. We prove that their existence is closely related to the existence of open G-orbits in multiple flag varieties and address the problem of classifying such series. Let G be a connected simply connected semisimple alge...

C5-decompositions of the tensor product of complete graphs

A Note on Tensor Product of Graphs

Let $G$ and $H$ be graphs. The tensor product $Gotimes H$ of $G$ and $H$ has vertex set $V(Gotimes H)=V(G)times V(H)$ and edge set $E(Gotimes H)={(a,b)(c,d)| acin E(G):: and:: bdin E(H)}$. In this paper, some results on this product are obtained by which it is possible to compute the Wiener and Hyper Wiener indices of $K_n otimes G$.