Shoumin Liu

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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 $ρ$ be a complex finite dimensional representation of $W$ . The characteristic polynomial o…

math.RT2021

Characteristic polynomials and finitely dimensional representations of $sl (2, C)$

Tianyi Jiang, Shoumin Liu

In this paper, we obtain a general formula for the characteristic polynomial of a finitely dimensional representation of Lie algebra $\mathfrak{sl}(2, \C )$ and the form for these…

The characteristic polynomials of imprimitive groups and affine Coxeter groups

Characteristic polynomials and some combinatorics for finite Coxeter groups

Characteristic polynomials and finitely dimensional representations of sl(2,C)

Characteristic polynomials and finitely dimensional representations of $sl (2, C)$