Tensor decompositions for SL(2) and outerplanar graphs

Tensor product decomposition rules for weight modules over the Hopf-Ore extensions of group algebras

In this paper, we investigate the tensor structure of the category of finite dimensional weight modules over the Hopf-Ore extensions $kG(χ^{-1}, a, 0)$ of group algebras $kG$. The tensor product decomposition rules for all indecomposable weight modules are explicitly given under the assumptions that $k$ is an algebraically closed field of characteristic zero, and the orders of $χ$ and $χ(a)$ are the same.

Cohomology and Decomposition of Tensor Product Representations of SL(2,R)

We analyze the decomposition of tensor products between infinite dimensional (unitary) and finite-dimensional (non-unitary) representations of SL(2,R). Using classical results on indefinite inner product spaces, we derive explicit decomposition formulae, true modulo a natural cohomological reduction, for the tensor products.

Decomposition of tensor products of modular irreducibles for $\SL_2$

We use tilting modules to study the structure of the tensor product of two simple modules for the algebraic group $\SL_2$, in positive characteristic, obtaining a twisted tensor product theorem for its indecomposable direct summands. Various other related results are obtained, and numerous examples are computed.

On tensor product decomposition of positive representations of $\mathcal{U}_{q\tilde{q}}(\mathfrak{sl}(2,\mathbb{R}))$

We study the tensor product decomposition of the split real quantum group $U_{q\tilde{q}}(sl(2,R))$ from the perspective of finite dimensional representation theory of compact quantum groups. It is known that the class of positive representations of $U_{q\tilde{q}}(sl(2,R))$ is closed under taking tensor product. In this paper, we show that one can derive the corresponding Hilbert space decomposition, given explicitly by quantum dilogarithm transformations, from the Clebsch-Gordan coefficients of the tensor product decomposition of finite dimensional representations of the compact quantum grou…

Unique decomposition of tensor products of irreducible representations of simple algebraic groups

We show that a tensor product of irreducible, finite dimensional representations of a simple Lie algebra over a field of characteristic zero, determines the individual constituents uniquely. This is analogous to the uniqueness of prime factorisation of natural numbers.

Probability measure near the boundary of tensor power decomposition for so(2n+1)

Character measure is a probability measure on irreducible representations of a semisimple Lie algebra. It appears from the decomposition into irreducibles of tensor power of a fundamental representation. In this paper we calculate the asymptotics of character measure on representations of so(2n+1) in the regime near the boundary of weight diagram. We find out that it converges to a Poisson-type distribution.

超越唯一性的张量分解及其在最小秩问题中的应用

Tensor decomposition beyond uniqueness, with an application to the minrank problem

本研究推广了欠完备场景下的Jennrich张量分解唯一性定理，提出矩阵-向量分解的定义，设计出高效随机算法求解最小分解，并将其应用于计算通用矩阵空间中的最小秩矩阵。

Multiplicity, Invariants and Tensor Product Decomposition of Tame Representations of U(\infty)

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 Bargmann-Segal-Fock spaces.