Reduction theorems for characters of finite groups of Lie type

Charles W. CURTIS

doi:10.2969/jmsj/02740666

Charles W. CURTIS

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JOURNAL FREE ACCESS

1975 Volume 27 Issue 4 Pages 666-688

DOI https://doi.org/10.2969/jmsj/02740666

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Published: 1975 Received: November 27, 1974 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) C. T. Benson and C. W. Curtis, On the degrees and rationality of certain characters of finite Chevalley groups, Trans. Amer. Math. Soc., 165 (1972), 251-273.
2) A. Borel, Linear Algebraic Groups, W. A. Benjamin, New York, 1969.
3) A. Borel, Properties and linear representations of Chevalley groups, Lecture Notes in Math., 131 (1970), Springer-Verlag, New York, 1-55.
4) N. Bourbaki, Groupes et algèbres de Lie, chap. 4, 5, 6, Paris, Hermann, 1968.
5) R. W. Carter and G. Lusztig, Modular representations of finite groups of Lie type, Proc. London Math. Soc., to appear.
6) R. W. Carter, Simple Groups of Lie Type, John Wiley & Sons, New York, 1972.
7) C. W. Curtis, N. Iwahori and R. Kilmoyer, Hecke algebras and characters of parabolic type of finite groups with (B, N)-pairs, Publ. Math. I. H. E. S., 40 (1972), 81-116.
8) C. W. Curtis, Corrections and additions to [1], Trans. Amer. Math. Soc., 202 (1975), 405-406.
9) C. W. Curtis, On the values of certain irreducible characters of finite Chevalley groups, 1st. Naz. di Alta Mat. Symp. Mat. XIII (1974), 343-355.
10) C. W. Curtis, Reduction theorems for characters of finite groups of Lie type, Proceedings, International Symposium on Finite Group Theory, Sapporo, Japan, 1974.
11) W. Feit, Characters of Finite Groups, W. A. Benjamin, New York, 1967.
12) P. Fong and G. M. Seitz, Groups with a (B, N)-pair of rank 2, I, Inv. Math., 21 (1973), 1-57; II, Inv. Math., 24 (1974), 191-239.
13) Harish-Chandra, Eisenstein series over finite fields, Functional Analysis and Related Fields, Springer-Verlag, 1970, 76-88.
14) R. Kilmoyer, Some irreducible complex representations of a finite group with a BN-pair, Ph. D. dissertation, M. I. T., 1969.
15) H. Nagao, A proof of Brauer's theorem on generalized decomposition numbers, Nagoya Math. J., 22 (1963), 73-77.
16) F. A. Richen, Modular representations of split (B, N)-pairs, Trans. Amer. Math. Soc., 140 (1969), 435-460.
17) L. L. Scott, Modular permutation representations, Trans. Amer. Math. Soc., 175 (1973), 101-121.
18) T. A. Springer, Cusp forms for algebraic groups, Lecture Notes in Math., 131 (1970), Springer-Verlag, New York, 97-120.
19) T. A. Springer, On the characters of certain finite groups, Proc. Summer School Group Repr., Budapest, 1971.

Right : [1] C. T. Benson and C. W. Curtis, On the degrees and rationality of certain characters of finite Chevalley groups, Trans. Amer. Math. Soc., 165 (1972), 251-273.
[2] A. Borel, Linear Algebraic Groups, W. A. Benjamin, New York, 1969.
[3] A. Borel, Properties and linear representations of Chevalley groups, Lecture Notes in Math., 131 (1970), Springer-Verlag, New York, 1-55.
[4] N. Bourbaki, Groupes et algèbres de Lie, chap. 4, 5, 6, Paris, Hermann, 1968.
[5] R. W. Carter and G. Lusztig, Modular representations of finite groups of Lie type, Proc. London Math. Soc., to appear.
[6] R. W. Carter, Simple Groups of Lie Type, John Wiley & Sons, New York, 1972.
[7] C. W. Curtis, N. Iwahori and R. Kilmoyer, Hecke algebras and characters of parabolic type of finite groups with (B, N)-pairs, Publ. Math. I. H. E. S., 40 (1972), 81-116.
[8] C. W. Curtis, Corrections and additions to [1], Trans. Amer. Math. Soc., 202 (1975), 405-406.
[9] C. W. Curtis, On the values of certain irreducible characters of finite Chevalley groups, 1st. Naz. di Alta Mat. Symp. Mat. XIII (1974), 343-355.
[10] C. W. Curtis, Reduction theorems for characters of finite groups of Lie type, Proceedings, International Symposium on Finite Group Theory, Sapporo, Japan, 1974.
[11] W. Feit, Characters of Finite Groups, W. A. Benjamin, New York, 1967.
[12] P. Fong and G. M. Seitz, Groups with a (B, N)-pair of rank 2, I, Inv. Math., 21 (1973), 1-57; II, Inv. Math., 24 (1974), 191-239.
[13] Harish-Chandra, Eisenstein series over finite fields, Functional Analysis and Related Fields, Springer-Verlag, 1970, 76-88.
[14] R. Kilmoyer, Some irreducible complex representations of a finite group with a BN-pair, Ph. D. dissertation, M. I. T., 1969.
[15] H. Nagao, A proof of Brauer's theorem on generalized decomposition numbers, Nagoya Math. J., 22 (1963), 73-77.
[16] F. A. Richen, Modular representations of split (B, N)-pairs, Trans. Amer. Math. Soc., 140 (1969), 435-460.
[17] L. L. Scott, Modular permutation representations, Trans. Amer. Math. Soc., 175 (1973), 101-121.
[18] T. A. Springer, Cusp forms for algebraic groups, Lecture Notes in Math., 131 (1970), Springer-Verlag, New York, 97-120.
[19] T. A. Springer, On the characters of certain finite groups, Proc. Summer School Group Repr., Budapest, 1971.

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