Identification of the irreducible modular representations of GLn(q)
Identification of the irreducible modular representations of GLn(q)
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GLn(q) 不可约模表示的识别
DOI：
10.1016/0021-8693(86)90215-2
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发表时间：
1986
影响因子：
0.9
通讯作者：
G. James
中科院分区：
文献类型：
--
作者：
R. Dipper;G. James
有限群(3)的表示理论中的一个基本事实是，G的普通不可约特征标的个数等于G的共轭类的个数。然而，在不可约特征标集和G的共轭类集之间通常不存在自然的双射，但在某些情况下仍然存在这样的双射。例如，如果G是对称群8，则特征标和共轭类都可以通过n的划分i以自然的方式索引。在他的基本文献[7]中，JA Green构造了有限一般线性群CL，(Q)的不等价普通不可约特征标，从而证明了在共轭类和普通不可约特征标之间本质上存在一个双射。双射中的唯一选择是以下列方式出现的。设GF(Q“‘)表示Q”的域！元素，并设GF(Q“！)*表示它的乘法群。
A basic fact in the representation theory of a finite group (3 is that the number of ordinary irreducible characters of G is equal to the number of conjugacy classes of G. However, there is usually no natural bijection between the set of irreducible characters and the set of conjugacy classes of G. None the less in some cases such a bijection exists. For example, if G is the symmetic group 8,, both the characters and conjugacy classes may be indexed in a natural way by partitions i of n. In his fundamental paper [7], JA Green constructed the inequivalent ordinary irreducible characters of the finite general linear group CL,,(q), showing on the way that there is essentially a bijection between the conjugacy classes and the ordinary irreducible characters. The only choice in the bijection arises in the following way. Let GF (q”‘) denote the field of q”! elements and let GF (q”!)* denote its multiplicative group.