On the degrees and rationality of certain characters of finite Chevalley groups

Authors:
C. T. Benson and C. W. Curtis

Journal:
Trans. Amer. Math. Soc. **165** (1972), 251-273

MSC:
Primary 20C30

DOI:
https://doi.org/10.1090/S0002-9947-1972-0304473-1

MathSciNet review:
0304473

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Abstract: Let be a system of finite groups with (*B, N*)-pairs, with Coxeter system (*W, R*) and set of characteristic powers (see [4]). Let *A* be the generic algebra of the system, over the polynomial ring . Let *K* be , *K* an algebraic closure of *K*, and the integral closure of in *K*. For the specialization mapping , let be a fixed extension of *f*. For each irreducible character of the algebra , there exists an irreducible character of the group in the system corresponding to q, such that , and is a bijective correspondence between the irreducible characters of and the irreducible constituents of . Assume almost all primes occur among the characteristic powers . The first main result is that, for each , there exists a polynomial such that, for each specialization , the degree is given by . The second result is that, with two possible exceptions in type , the characters are afforded by rational representations of .

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DOI:
https://doi.org/10.1090/S0002-9947-1972-0304473-1

Keywords:
Finite group,
(*B,N*)-pair,
Coxeter group,
generic algebra,
irreducible character,
generic degree

Article copyright:
© Copyright 1972
American Mathematical Society