Representation Dimension and Solomon Zeta Function

利用局部ζ积分计算表代数序的ζ函数

Computing zeta functions of table algebra orders using local zeta integrals

针对Solomon初等方法计算秩≥3的整表代数序的ζ函数存在困难的问题，研究了用Bushnell和Reiner的局部ζ积分法计算这类序的显式ζ函数，并给出了应用示例。

Modular Lie powers and the Solomon descent algebra

Let $V$ be an $r$-dimensional vector space over an infinite field $F$ of prime characteristic $p$, and let $L_n(V)$ denote the $n$-th homogeneous component of the free Lie algebra on $V$. We study the structure of $L_n(V)$ as a module for the general linear group $GL_r(F)$ when $n=pk$ and $k$ is not divisible by $p$ and where $n \geq r$. Our main result is an explicit 1-1 correspondence, multiplicity-preserving, between the indecomposable direct summands of $L_k(V)$ and the indecomposable direct summands of $L_n(V)$ which are not isomorphic to direct summands of $V^{\otimes n}$. The direct sum…