Related papers: Covering $\mathsf{Irrep}(S_n)$ With Tensor Product…
We explicitly calculate the triangle inequalities for the group PSO(8). Therefore we explicitly solve the eigenvalues of sum problem for this group (equivalently describing the side-lengths of geodesic triangles in the corresponding…
The aim of this work is to study finite dimensional representations of the Lie superalgebra psl(2|2) and their tensor products. In particular, we shall decompose all tensor products involving typical (long) and atypical (short)…
A new connection between two different necessary conditions for a polymatroid to be linearly representable is presented. Specifically, we prove that the existence of a tensor product with the uniform matroid of rank two on three elements…
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…
In this paper we completely characterise irreducible tensor products of representations of alternating groups in characteristic 2 of a basic spin module with an irreducible module. This completes the classification of irreducible tensor…
We consider the Plancherel measure on irreducible components of tensor powers of the spinor representation of so(2n+1). The irreducible representations correspond to the generalized Young diagrams. With respect to this measure the…
We study the remarkable Saxl conjecture which states that tensor squares of certain irreducible representations of the symmetric groups S_n contain all irreducibles as their constituents. Our main result is that they contain representations…
The $\star_M$-family of tensor-tensor products is a framework which generalizes many properties from linear algebra to third order tensors. Here, we investigate positive semidefiniteness and semidefinite programming under the…
We describe the tensor products of two irreducible linear complex representations of the finite general linear group G = GL(3,q) in terms of induced representations by linear characters of maximal torii and also in terms of Gelfand-Graev…
We present a conjecture on the irreducibility of the tensor products of fundamental representations of quantized affine algebras. This conjecture implies in particular that the irreducibility of the tensor products of fundamental…
We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…
Following up on a previous analysis of graph embeddings, we generalize and expand some results to the general setting of vector symbolic architectures (VSA) and hyperdimensional computing (HDC). Importantly, we explore the mathematical…
The aim of this note is to point out a convexity property with respect to the root lattice for the support of the highest weights that occur in a tensor product of irreducible rational representations of $SL(n)$ over the complex numbers.…
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 show that in a finite tensor category, the tensor product property holds for support varieties if and only if it holds between indecomposable periodic objects. We apply this to certain Hopf algebras in the form of skew group algebras. In…
We establish the existence of an irreducible representation of $A_n$ whose dimension does not occur as the dimension of an irreducible representation of $S_n$, and vice versa. This proves a conjecture by Tong-Viet. The main ingredient in…
From an irreducible representation of GL(n, C) there is a natural way to construct an irreducible representations of GL(n + 1, C) by adding a zero at the end of the highest weight of the irreducible representation of GL(n, C). The paper…
We construct categorifications of tensor products of arbitrary finite-dimensional irreducible representations of $\mathfrak{sl}_k$ with subquotient categories of the BGG category $\mathcal{O}$, generalizing previous work of Sussan and…
In this paper, we give a construction of certain induced complementary series of the universal covering of the symplectic groups. There are abundant such representations besides those of linear groups. We achieve this by applying invariant…
We classify indecomposable summands of mixed tensor powers of the natural representation for the general linear supergroup up to isomorphism. We also give a formula for the characters of these summands in terms of composite supersymmetric…