On the degrees and rationality of certain characters of finite Chevalley groups
On the degrees and rationality of certain characters of finite Chevalley groups
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有限Chevalley群某些特征的度和合理性
DOI：
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发表时间：
1972
期刊：
影响因子：
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通讯作者：
C. Curtis
中科院分区：
文献类型：
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作者：
C. T. Benson;C. Curtis
。令 a' 为具有 (5, N) 对的有限群系统，具有 Coxeter 系统 (W, R) 和特征幂集 {q}（参见 [4]）。令 A 为系统在多项式环 o—Q[u] 上的泛代数。令 K 为 ß(w)，K 为 K 的代数闭包，o* 为 K 中 o 的积分闭包。对于特化 /：«->-<？映射o -*■ Q，令/* : o* -> Q 为/ 的固定扩展。对于代数 As 的每个不可约字符 x，都存在一个不可约字符 £,,,。对应于q的系统中群G(q)的，使得(£»,/•,lf<S))>0，且x -*■ ix.r是A*的不可约特征与lg$的不可约成分之间的双射对应。假设几乎所有素数都出现在特征幂 {q} 中。第一个主要结果是，对于每个 x，都存在一个多项式 dx(t) e Q [/]，这样，对于每个特化 /: u^-q，度 {,,/•(!) 由 dx{q) 给出。第二个结果是，除了类型 E7 中的两个可能的例外之外，字符 £/t/。由 G(q) 的有理表示提供。
. Let a' be a system of finite groups with (5, N)-pairs, with Coxeter system (W, R) and set of characteristic powers {q} (see [4]). Let A be the generic algebra of the system, over the polynomial ring o—Q[u]. Let K be ß(w), K an algebraic closure of K, and o* the integral closure of o in K. For the specialization /: «->-<? mapping o -*■ Q, let/* : o* -> Q be a fixed extension of/. For each irreducible character x of the algebra As, there exists an irreducible character £,,,. of the group G{q) in the system corresponding to q, such that (£»,/•, lf<S))>0, and x -*■ ix.r is a bijective correspondence between the irreducible characters of A* and the irreducible constituents of lg$. Assume almost all primes occur among the characteristic powers {q}. The first main result is that, for each x, there exists a polynomial dx(t) e Q [/] such that, for each specialization /: u^-q, the degree {,,/•(!) is given by dx{q). The second result is that, with two possible exceptions in type E7, the characters £/t/. are afforded by rational representations of G(q).