Related papers: On tensor products of polynomial representations

Let $R$ be a principal ideal local ring of finite length with a finite residue field of odd characteristic. Let $G(R)$ denote either the general linear group or the general unitary group of degree two over $R$. We study the decomposition of…

The Littlewood-Richardson coefficients $c^\nu_{\lambda,\mu}$ are the multiplicities in the tensor product decomposition of two irreducible representations of the general linear group GL$(n, {\mathbb C})$. They are parametrized by the…

We introduce the honeycomb model of BZ polytopes, which calculate Littlewood-Richardson coefficients, the tensor product rule for GL(n). Our main result is the existence of a particularly well-behaved honeycomb with given boundary…

In this paper, we study the tensor product of two unitary irreducible representations, as well as the tensor product of a unitary irreducible representation with a finite-dimensional one, and determine the corresponding Clebsch-Gordan…

To facilitate a simultaneous treatment of an arbitrary number of colors in representation theory-based descriptions of QCD color structure, we derive an $N$-independent reduction of SU($N$) tensor products. To this end, we label each…

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 Littlewood-Richardson coefficients $c^{\lambda}_{\mu\nu}$ give the multiplicity of an irreducible polynomial ${\rm GL}_n$-representation $F^{\lambda}_n$ in the tensor product of polynomial representations $F^{\mu}_n\otimes F^{\nu}_n$.…

We give universal upper bounds on the relative dimensions of isotypic components of a tensor product of the linear group GL(n) representations and universal upper bounds on the relative dimensions of irreducible components of a tensor…

We give a geometric proof of a conjecture of W. Fulton on the multiplicities of irreducible representations in a tensor product of irreducible representations for GL(r).

We consider the quantum double D(G) of a compact group G, following an earlier paper. We use the explicit comultiplication on D(G) in order to build tensor products of irreducible *-representations. Then we study their behaviour under the…

In this paper we study irreducible tensor products of representations of alternating groups in characteristics 2 and 3. In characteristic 3 we completely classify irreducible tensor products, while in characteristic 2 we completely classify…

We formulate a series of conjectures on the stable tensor product of irreducible representations of symmetric groups, which are closely related to the reduced Kronecker coefficients. These conjectures are certain generalizations of…

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…

In this short note, we give a new sufficient condition for a linear map from a product of copies of a field to endomorphisms of a finite dimensional vector space over the same field to be an algebra homomorphism. We expect that this result…

In this paper, we consider the necessary and sufficient conditions for the tensor product of the fundamental representations for the restricted quantum loop algebras of type A at roots of unity to be irreducible.

We investigate the homogeneous $2$-local representations of the twin group $T_n$ for all integers $n\geqslant 2$. A complete classification is obtained, yielding three distinct families of representations. We show that each of these…

We introduce a family of rings of symmetric functions depending on an infinite sequence of parameters. A distinguished basis of such a ring is comprised by analogues of the Schur functions. The corresponding structure coefficients are…

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…

We give a necessary and sufficient condition for a pair of parabolic subgroups $P$ and $Q$ of $G=GL_n(\mathbb{R})$ such that the tensor product of any two unitarily induced representations from $P$ and $Q$ are tempered. We also give an…

Let $G$ be a finitely generated group. We prove that the $n$-fold tensor product $G^{\otimes n}$ is finite (resp. polycyclic) if and only $G$ is finite (resp. polycyclic). Further, assuming that $G$ is finitely presented, we show that…