Related papers: Tensor invariants of SL(n), wave graphs and L-tris

Using semi-tensor product of matrices, the structures of several kinds of symmetric games are investigated via the linear representation of symmetric group in the structure vector of games as its representation space. First of all, the…

This is a note for constructing fundamental invariants and computing the Hilbert series of the invariant subalgebras of tensor products of polynomial rings under the action by a direct product of symmetric groups. Our computation relies on…

We present the relativistic hydrostatic equilibrium equations for a wide class of gravitational theories possessing a scalar-tensor representation. It turns out that the stellar structure equations can be written with respect to the…

Let K be the product O(n_1) x O(n_2) x ... x O(n_r) of orthogonal groups. Let V the r-fold tensor product of defining representations of each orthogonal factor. We compute a stable formula for the dimension of the K-invariant algebra of…

Let V be a finite-dimensional superspace and G a simple (or a ``close'' to simple) matrix Lie superalgebra, i.e., a Lie subsuperalgebra in GL(V). Under the classical invariant theory for G we mean the description of G-invariant elements of…

For several objects of interest in geometric complexity theory, namely for the determinant, the permanent, the product of variables, the power sum, the unit tensor, and the matrix multiplication tensor, we introduce and study a fundamental…

We determine the necessary and sufficient combinatorial conditions for which the tensor product of two irreducible polynomial representations of $GL(n,\mathbb{C})$ is isomorphic to another. As a consequence we discover families of…

We use the method of the tensor product graph to construct rational (Yangian invariant) solutions of the Yang-Baxter equation in fundamental representations of $c_n$ and thence the full set of $c_n$-invariant factorized $S$-matrices. Brief…

We introduce a common generalization of the L-R-smash product and twisted tensor product of algebras, under the name L-R-twisted tensor product of algebras. We investigate some properties of this new construction, for instance we prove a…

The structure of r-fold tensor products of irreducible tame representations of the inductive limit U(\infty) of unitary groups U(n) are are described, versions of contragredient representations and invariants are realized on…

A complete classification of \(\mathrm{SL}(n)\) contravariant, \(p\)-order tensor valuations on convex polytopes in \( \mathbb{R}^n \) for \( n \geq p \) is established without imposing additional assumptions, particularly omitting any…

Neural networks that satisfy invariance with respect to input permutations have been widely studied in machine learning literature. However, in many applications, only a subset of all input permutations is of interest. For heterogeneous…

Invariant tensors play an important role in gauge theories, for example, in dualities of N=1 gauge theories. However, for theories with fields in representations larger than the fundamental, the full set of invariant tensors is often…

A "tensor space" is a vector space equipped with a finite collection of multi-linear forms. In previous work, we showed that (for each signature) there exists a universal homogeneous tensor space, which is unique up to isomorphism. Here we…

This article is a continuation of work on construction and calculation various of modifications of invariant based on the use Euclidean metric values attributed to elements of manifold triangulation. We again address the well investigated…

The symmetric tensor power of graphs is introduced and its fundamental properties are explored. A wide range of intriguing phenomena occur when one considers symmetric tensor powers of familiar graphs. A host of open questions are…

The signature of a path is a sequence of tensors whose entries are iterated integrals, playing a key role in stochastic analysis and applications. The set of all signature tensors at a particular level gives rise to the universal signature…

We associate a moduli problem to a colored trivalent graph; such graphs, when planar, appear in the state-sum description of the quantum sl(N) knot polynomial due to Murakami, Ohtsuki, and Yamada. We discuss how the resulting moduli space…

We introduce a nonsymmetric, associative tensor product among representations of Cuntz algebras by using embeddings. We show the decomposition formulae of tensor products for permutative representations explicitly We apply decomposition…

One of the apparent advantages of quantum computers over their classical counterparts is their ability to efficiently contract tensor networks. In this article, we study some implications of this fact in the case of topological tensor…