Related papers: A Basis for the GL_n Tensor Product Algebra

We introduce a new topological coproduct $\Delta^{\psi}_{u}$ for quantum toroidal algebras $U_{q}(\mathfrak{g}_{\mathrm{tor}})$ in all untwisted types, leading to a well-defined tensor product on the category…

We introduce a non-symmetric tensor product of representations of UHF algebras by using Kronecker products of matrices. We prove tensor product formulae of GNS representations by product states and show examples.

In this paper, we will present a generalization of the L-tensor product (L-product) including generalization of the well known tensor cosine and T-products that were defined for third-order tensors and based on fast Fourier transform and…

By a tensor we mean an element of a tensor product of vector spaces over a field. Up to a choice of bases in factors of tensor products, every tensor may be coordinatized, that is, represented as an array consisting of numbers. This note is…

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).

Given a quantized enveloping algebra $U_q(\mathfrak g)$ and a pair of dominant weights ($\lambda$, $\mu$), we extend a conjecture raised by Lusztig in \cite{Lusztig:1992}to a more general form and then prove this extended Lusztig's…

The minimal irreducible representations of $U_q[gl(m|n)]$, i.e. those irreducible representations that are also irreducible under $U_q[osp(m|n)]$ are investigated and shown to be affinizable to give irreducible representations of the…

We study the decomposition of tensor products between a Steinberg module and a costandard module, both as a module for the algebraic group $G$ and when restricted to either a Frobenius kernel $G_r$ or a finite Chevalley group…

We consider the structure of algebra of operators, acting in $n-$fold tensor product space, which are partially transposed on the last term. Using purely algebraical methods we show that this algebra is semi-simple and then, considering its…

We study a family of complex representations of the group GL(n,O), where O is the ring of integers of a non-archimedean local field F. These representations occur in the restriction of the Grassmann representation of GL(n,F) to its maximal…

We generalize a construction in [BW18] (arXiv:1610.09271) by showing that the tensor product of a based $\textbf{U}^{\imath}$-module and a based $\textbf{U}$-module is a based $\textbf{U}^{\imath}$-module. This is then used to formulate a…

The decomposition of tensor products of representations into irreducibles is studied for a continuous family of integrable operator representations of $U_q(sl(2,R)$. It is described by an explicit integral transformation involving a…

Classical Clifford theory studies the decomposition of simple $G$-modules into simple $H$-modules for some normal subgroup $H \triangleleft G$. In this paper we deal with chains of normal subgroups $1 \triangleleft G_1 \triangleleft \cdots…

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…

A reduction formula for the branching coefficients of tensor products of representations and more generally restrictions of representations of a semisimple group to a semisimple subgroup is proved in work by Knutson-Tao and Derksen-Weyman.…

Here is discussed generalization of Clifford algebras, l^n-dimensional Weyl-Clifford algebras T(n,l) with n generators t_k satisfying equation $(\sum_{k=1}^n a_k t_k)^l = \sum_{k=1}^n a_k^l$. It is originated from two basic and well known…

We give a description of the image of tensor products of tautological bundles on Hilbert schemes of points on surfaces under the Bridgeland-King-Reid-Haiman equivalence. Using this, some new formulas for cohomological invariants of these…

We initiate a study of infinite tensor products of projective unitary representations of a discrete group G. Special attention is given to regular representations twisted by 2-cocycles and to projective representations associated with…

Tensor products of irreducible representations of the Jordanian quantum algebras U_h(sl(2)) and U_h(su(1,1)) are considered. For both the highest weight finite dimensional representations of U_h(sl(2)) and lowest weight infinite dimensional…

In past few decades, tensor algebra also known as multi-linear algebra has been developed and customized as a tool to be used for various engineering applications. In particular, with the help of a special form of tensor contracted product,…