Zeros and roots of unity in character tables

特征标表中零点与单位根稠密性的结果

Denseness results for zeros and roots of unity in character tables

本文证明了有限群不可约特征标取值中零点与单位根元素占比在区间[1/2,1]内具有稠密性，即对任意目标比例和误差均可构造出相应的不可约特征标。

Irreducible characters taking root of unity values on p-singular elements

In this paper we study finite p-solvable groups having irreducible complex characters chi in Irr(G) which take roots of unity values on the p-singular elements of G.

Group elements whose character values are roots of unity

We classify all finite groups $G$ which possesses an element $x\in G$ such that every irreducible character of $G$ takes a root of unity value at $x$.

Irreducible representations of q-Schur superalgebras at a root of unity

Under the assumption that the quantum parameter $q$ is an $l$-th primitive root of unity with $l$ odd in a field $F$ of characteristic 0 and $m+n\geq r$, we obtained a complete classification of irreducible modules of the $q$-Schur superalgebra introduced H. Rui and the first Author.

Image of the Burau Representation at $d$-th Roots of unity

We prove that the image of the Full braid group $B_{n+1}$ on $n+1$ strands under the Burau representation, evaluated at a primitive $d$-th root of unity is arithmetic provided $n\geq d$.

关于在非单位元素上的值为至多两个单位根之和的广义特征标

On Generalized Characters Whose Values on Nonidentity Elements are Sums of at Most Two Roots of Unity

本文研究了阿贝尔群上在非单位元素处取值为至多两个单位根之和的广义特征标，描述了其不可约成分，并应用该结果揭示了容许此类特征标的群的素图连通性。