Character Products and Q-Polynomial Group Association Schemes☆
Character Products and Q-Polynomial Group Association Schemes☆
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字符积与Q多项式群关联方案☆
DOI：
10.1006/jabr.1999.8205
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发表时间：
1998
影响因子：
0.9
通讯作者：
H. Suzuki
中科院分区：
文献类型：
--
作者：
Masao Kiyota;H. Suzuki
摘要研究了一个具有忠实特征标的有限群，它的平方有少量的不可约特征标作为成分。设IRR(G)是有限群G的绝对不可约普通特征标的集合，对每个φ，∈，IRR(G)，设φ=φ，如果φ是实值的，则φ=φ，+φ，其中φ表示φ的复共轭.设Rirr(G)=φ{φ|∈(G)}。对于χ，∈和Rirr(G)，设χ2=b·1+a·χ+Ψ，使得Ψ是G的一个字符，它既不包含χ，也不包含主要字符1作为成分。我们研究了当Ψ是IRRR(G)中关于Galois群Gal(Q/Q(χ))的作用在单一轨道上的特征标之和的数量倍数的情况。这里Q表示Q在C中的代数闭包，Q(χ)是由χ的值生成的域。作为应用，我们给出了q-多项式群结合方案的一个分类。
Abstract We study a finite group having a faithful character whose square has a small number of irreducible characters as constituents. Let Irr(G) be the set of absolutely irreducible ordinary characters of a finite group G. For each φ ∈ Irr(G), let φ = φ if φ is real valued and φ = φ + φ otherwise, where φ denotes the complex conjugate of φ. Let RIrr(G) = {φ | φ ∈ Irr(G)}. For χ ∈ RIrr(G), let χ 2 = b · 1 + a · χ + Ψ such that Ψ is a character of G which does not contain χ nor the principal character 1 as a constituent. We study the case when Ψ is a scalar multiple of a sum of the characters in IRrr(G), which are in a single orbit with respect to the action of the Galois group Gal(Q/Q(χ)). Here Q denotes the algebraic closure of Q in C and Q(χ) is the field generated by the values of χ. As an application, we give a classification of Q-polynomial group association schemes.