Composition Factors of Tensor Products of Symmetric Powers

Composition factors of 2-parts spin representations of symmetric groups

Given an odd prime $p$, we identify composition factors of the reduction modulo $p$ of spin irreducible representations of the covering groups of symmetric groups indexed by partitions with 2 parts and find some decomposition numbers.

Composition Factors of Tensor Products of Truncated Symmetric Powers

Let $G$ be the general linear group of degree $n$ over an algebraically closed field $K$ of characteristic $p>0$. We study the $m$-fold tensor product $\bar{S}(E)^{\otimes m}$ of the truncated symmetric algebra $\bar{S}(E)$ of the symmetric algebra $S(E)$ of the natural module $E$ for $G$. We are particularly interested in the set of partitions $λ$ occurring as the highest weight of a composition factor of $\bar{S}(E)^{\otimes m}$. We explain how the determination of these composition factors is related to the determination of the set of composition factors of the $m$-fold tensor product $S(E)…

Irreducible tensor products of representations of covering groups of symmetric and alternating groups

In this paper we completely classify irreducible tensor products of covering groups of symmetric and alternating groups in characteristic $\not=2$.

Irreducible tensor products for symmetric groups in characteristic 2

We consider non-trivial irreducible tensor products of modular representations of a symmetric group $S_n$ in characteristic 2 for even $n$ completing the proof of a classification conjecture of Gow and Kleshchev about such products.

On the decomposition of tensor representations of symmetric groups

Following the general idea of Schur--Weyl scheme and using two suitable symmetric groups (instead of one), we try to make more explicit the classical problem of decomposing tensor representations of finite and infinite symmetric groups into irreducible components.

GL(n)的张量积合成重数与分支重数

Composition Multiplicities of Tensor Products and Branching Multiplicities for $\text{GL}(n)$

本文在Brundan-Kleshchev工作基础上，研究GL(n)单模与对偶自然模外积平方的张量积，建立了合成重数与分支重数之间的联系，并给出计算部分合成重数的方法。