Irreducible constituents of minimal degree in supercharacters of the finite unitriangular groups
Irreducible constituents of minimal degree in supercharacters of the finite unitriangular groups
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DOI：
10.1016/j.jpaa.2014.09.016
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发表时间：
2013-11
影响因子：
0.8
通讯作者：
R. Dipper;Qiong Guo
中科院分区：
文献类型：
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作者：
R. Dipper;Qiong Guo
设q是素数幂，U是某个自然数n的n阶下单三角矩阵群.我们给出了André-Yan超字符的不可约成分的度的一个下界，并对具有其度假定为这个下界的成分的超字符进行了分类。此外，我们证明了满足这个条件的U的不同不可约特征标的个数是（q− 1）中具有非负整系数的多项式，并展示了这些多项式的单项源。
Let q be a prime power and U the group of lower unitriangular matrices of order n for some natural number n. We give a lower bound for the degrees of irreducible constituents of André–Yan supercharacters and classify the supercharacters having constituents whose degree assume this lower bound. Moreover we show that the number of distinct irreducible characters of U meeting this condition is a polynomial in (q− 1) with nonnegative integral coefficients and exhibit monomial sources for those.