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On the degrees and rationality of certain characters of finite Chevalley groups. (English) Zbl 0246.20008

MSC:
20C30 Representations of finite symmetric groups
20C15 Ordinary representations and characters
20G05 Representation theory for linear algebraic groups
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[1] M. Benard, On the Schur indices of the characters of the exceptional Weyl groups, Ph.D. Dissertation, Yale University, New Haven, Conn., 1969. · Zbl 0202.02903
[2] R. Carter, Conjugacy classes in the Weyl group, Seminar on Algebraic Groups and Related Finite Groups (The Institute for Advanced Study, Princeton, N.J., 1968/69) Springer, Berlin, 1970, pp. 297 – 318.
[3] Charles W. Curtis and Timothy V. Fossum, On centralizer rings and characters of representations of finite groups, Math. Z. 107 (1968), 402 – 406. · Zbl 0185.06801 · doi:10.1007/BF01110070 · doi.org
[4] C. W. Curtis, N. Iwahori, and R. Kilmoyer, Hecke algebras and characters of parabolic type of finite groups with (\?, \?)-pairs, Inst. Hautes √Čtudes Sci. Publ. Math. 40 (1971), 81 – 116. · Zbl 0254.20004
[5] Charles W. Curtis and Irving Reiner, Representation theory of finite groups and associative algebras, Pure and Applied Mathematics, Vol. XI, Interscience Publishers, a division of John Wiley & Sons, New York-London, 1962. · Zbl 0131.25601
[6] T. V. Fossum, Characters and centers of symmetric algebras, J. Algebra 16 (1970), 4 – 13. · Zbl 0212.05903 · doi:10.1016/0021-8693(70)90036-0 · doi.org
[7] Ronald Forrest Fox, A simple new method for calculating the characters of the symmetric groups, J. Combinatorial Theory 2 (1967), 186 – 212. · Zbl 0153.03802
[8] J. S. Frame, The classes and representations of the groups of 27 lines and 28 bitangents, Ann. Mat. Pura Appl. (4) 32 (1951), 83 – 119. · Zbl 0045.00505 · doi:10.1007/BF02417955 · doi.org
[9] -, The characters of the Weyl group \( {E_8}\), Computational Problems in Abstract Algebra (Proc. Conf. Oxford, 1967), Pergamon, Oxford, 1970, pp. 111-130.
[10] P. X. Gallagher, Group characters and normal Hall subgroups, Nagoya Math. J. 21 (1962), 223 – 230. · Zbl 0114.25603
[11] G. J. Janusz, Primitive idempotents in group algebras, Proc. Amer. Math. Soc. 17 (1966), 520 – 523. · Zbl 0151.02203
[12] Takeshi Kondo, The characters of the Weyl group of type \?\(_{4}\), J. Fac. Sci. Univ. Tokyo Sect. I 11 (1965), 145 – 153 (1965). · Zbl 0132.27401
[13] Serge Lang, Diophantine geometry, Interscience Tracts in Pure and Applied Mathematics, No. 11, Interscience Publishers (a division of John Wiley & Sons), New York-London, 1962. · Zbl 0115.38701
[14] F. D. Murnaghan, The theory of group representations, Johns Hopkins Press, Baltimore, Maryland, 1938. · Zbl 0022.11807
[15] Tadasi Nakayama, Some studies on regular representations, induced representations and modular representations, Ann. of Math. (2) 39 (1938), no. 2, 361 – 369. · Zbl 0020.34103 · doi:10.2307/1968792 · doi.org
[16] T. A. Springer, Cusp forms for finite groups, Seminar on Algebraic Groups and Related Finite Groups (The Institute for Advanced Study, Princeton, N.J., 1968/69) Lecture Notes in Mathematics, Vol. 131, Springer, Berlin, 1970, pp. 97 – 120.
[17] R. Steinberg, A geometric approach to the representations of the full linear group over a Galois field, Trans. Amer. Math. Soc. 71 (1951), 274 – 282. · Zbl 0045.30201
[18] -, Lectures on Chevalley groups, Lecture Notes, Yale University, New Haven, Conn., 1967.
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