A family of polynomials related to generic degrees

一类不能作为可解群特征标度图的图族

A family of graphs that cannot occur as character degree graphs of solvable groups

本文研究可解群的特征标度图，给出排除某些度图可实现性的一般性结果，并证明一类具体图族不能作为任何可解群的特征标度图。

On the E-polynomials of a family of Character Varieties

We compute the E-polynomials of a family of twisted character varieties by proving they have polynomial count, and applying a result of N. Katz on the counting functions. To compute the number of GF(q)-points of these varieties as a function of q, we used a formula of Frobenius. Our calculations made use of the character tables of Gl(n,q) and Sl(n,q), previously computed by J. A. Green and G. Lehrer, and a result of Hanlon on the Möbius function of a subposet of set-partitions. The Euler Characteristics of these character varieties are calculated with these polynomial.

单位根扭转的带标志斜Schur多项式

Flagged Skew Schur Polynomials Twisted By Roots Of Unity

本研究推广了Littlewood的Schur多项式因式分解定理，证明一类带标志斜Schur多项式在变量被单位根扭转时也有类似因式分解，且包含Demazure特征标作为特例。

关于特征标次数多项式的一个注记

A note on polynomials for character degrees

本文针对对称群特征标次数的Rasala多项式展开，提出了一种简短的代数证明替代方法，并将其推广至特征标值的多项式。

一族无穷次 tt-环

A family of infinite degree tt-rings

本文构造了一族无穷次 tt-环，从而对 P. Balmer 提出的一个公开问题给出了否定回答。

The degree of the Hilbert-Poincaré polynomial of PBW-graded modules

In this note, we study the Hilbert-Poincaré polynomials for the PBW-graded of simple modules for a simple complex Lie algebra. The computation of their degree can be reduced to modules of fundamental highest weight. We provide these degrees explicitly.