Shoumin Liu

collaborators

4 papers

math.RT2025

Coxeter groups and the proper joint spectrums of their faithful representations

Shoumin Liu, Zhaohuan Peng, Xumin Wang

In this paper, we analyze the faithful representations of the dihedral groups, and prove that the Coxeter groups can be determined by the proper joint spectrum of their faithful re…

math.RT2025

The characteristic polynomials of imprimitive groups and affine Coxeter groups

Chenyue Feng, Shoumin Liu, Xumin Wang

In this paper, we will seek appropriate generators to define the characteristic polynomials of $G (r, 1, n)$ , and prove that for every finite dimensional representation of $G (r, 1, n)$ ,…

math.RT2025

Characteristic polynomials and some combinatorics for finite Coxeter groups

Shoumin Liu, Yuxiang Wang

Let $W$ be a finite Coxeter group with Coxeter generating set $S = {s_{1}, \dots, s_{n}}$ , and $I ¨ $ be a complex finite dimensional representation of $W$ . The characteristic polynomial…

math.RT2024

Characteristic polynomials for classical Lie algebras

Chenyue Feng, Shoumin Liu, Xumin Wang

In this paper, we will compute the characteristic polynomials for finite dimensional representations of classical complex Lie algebras and the exceptional Lie algebra of type G2, w…