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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

Representations of finite groups of Lie type

Author(s): Charles W. Curtis
Journal: Bull. Amer. Math. Soc. 1 (1979), 721-757.
MSC (1970): Primary 20C15; Secondary 20G05, 20G40
MathSciNet review: 537625
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References:

[I1] F. G. Frobenius, Gesammelte Abhandlungen, Bd. 1, 2, 3, Springer-Verlag, Berlin, 1968. MR 235974

[I2] G. Warner, Harmonic analysis on semi-simple Lie groups. I, II, Die Grundlehren der Math. Wissenschaften, Bd. 188, 189, Springer-Verlag, New York, 1970. MR 498999

[I3] A. Young, Quantitative substitutional analysis. I-VIII, Proc. London Math. Soc. (1) 33 (1901), 97-146; (1) 34 (1902), 361-397; (2) 28 (1928), 255-292; (2) 31 (1930), 253-272; (2) 31 (1930), 273-288; (2) 34 (1932), 196-230; (2) 36 (1933), 304-368; (2) 37 (1934), 441-495.

1.
C. T. Benson, On the generic algebra of a unipotent subgroup of a finite Chevalley group, Comm. Algebra (to appear). MR 447421
2.
C. T. Benson, The generic degrees of the irreducible characters of E8, Comm. Algebra (to appear). MR 535928
3.
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; 202 (1975), 405-406. MR 304473
4.
C. T. Benson, L. C. Grove and D. B. Surowski, Semilinear automorphisms and dimension functions for certain characters of finite Chevalley groups, Math. Z. 144 (1977), 149-159. MR 382468
5.
A. Borel, Linear algebraic groups, Benjamin, New York, 1969. MR 251042
6.
A. Borel, Properties and linear representations of Chevalley groups, Part A, Seminar on Algebraic Groups and Related Finite Groups, Lecture Notes in Math., vol. 131, Springer-Verlag, Berlin and New York, 1970. MR 258838
7.
A. Borel and J. Tits, Groupes reductifs, Inst. Hautes Études Sci. Publ. Math. 27 (1965), 55-151. MR 207712
8.
A. Borel and J. Tits, Elements unipotents et sous-groupes paraboliques de groupes reductifs. I, Invent. Math. 12 (1971), 95-104. MR 294349
9.
N. Bourbaki, Groupes et algèbres de Lie, Chaps. 4-6, Actualités Sci. Indust. no. 1337, Hermann, Paris, 1968. MR 240238
10.
R. W. Carter, Conjugacy classes in the Weyl groups, Compositio Math. 25 (1972), 1-59. MR 318337
11.
R. W. Carter, Simple groups of Lie type, Wiley, New York and London, 1972. MR 407163
12.
R. W. Carter, Centralizers of semisimple elements infinite groups of Lie type, Proc. London Math. Soc. (3) 37 (1978), 491-507. MR 512022
13.
B. Chang and R. Ree, The characters of G2(q), Istituto Nazionale di Alta Matematica, Symposia Mathematica, vol. 13, 1974, pp. 395-413. MR 364419
14.
C. Chevalley, Sur certains groupes simples, Tôhoku Math. J. 7 (1955), 14-66. MR 73602
15.
C. Chevalley, Classification des groupes de Lie algébriques, Paris, 1956/1958.
16.
C. W. Curtis, The Steinberg character of a finite group with a (B, N)-pair, J. Algebra 4 (1966), 433-441. MR 201524
17.
C. W. Curtis, On the values of certain irreducible characters of finite Chevalley groups, Istituto Nazionale di Alta Matematica, Symposia Mathematica, vol. 13, 1974, pp. 343-355. MR 369561
18.
C. W. Curtis, Reduction theorems for characters of finite groups of Lie type, J. Math. Soc. Japan 27 (1975), 666-688. MR 399282
19.
C. W. Curtis, A note on the connections between the generalized characters of Deligne and Lusztig and the cuspidal characters of reductive groups over finite fields, J. London Math. Soc. 14 (1976), 405-412. MR 435238
20.
C. W. Curtis and T. Fossum, On centralizer rings and characters of representations of finite groups, Math. Z. 107 (1968), 402-406. MR 237665
21.
C. W. Curtis, N. Iwahori and R. Kilmoyer, Hecke algebras and characters of parabolic type of finite groups with (B, N)-pairs, Inst. Hautes Études Sci. Publ. Math. 40 (1972), 81-116. MR 347996
22.
C. W. Curtis, W. M. Kantor and G. M. Seitz, The 2-transitive permutation representations of the finite Chevalley groups, Trans. Amer. Math. Soc. 218 (1976), 1-59. MR 422440
23.
C. W. Curtis and G. I. Lehrer, The homology of certain fixed point sets in the Tits complex of a reductive group over a finite field (to appear).
24.
P. Deligne, Cohomologie Étale, Sem. de Géométrie Alg. du Bois Marie SGA 4${1øver 2}$, Lecture Notes in Math., vol. 569, Springer-Verlag, Berlin and New York, 1977. MR 463174
25.
P. Deligne and G. Lusztig, Representations of reductive groups over finite fields, Ann. of Math. (2) 103 (1976), 103-161. MR 393266
26.
L. E. Dickson, Linear groups, Dover, New York, 1958. MR 104735
27.
J. Dieudonné, La géométrie des groupes classiques, Ergebnisse der Math. und ihrer Grenzgebiete, vol. 5, Springer-Verlag, Berlin and New York, 1955. MR 72144
28.
H. Enomoto, The characters of the finite Chevalley groups G2(q), q = 3+, Japan. J. Math. (N.S.) 2 (1976), 191-248. MR 437628
29.
P. Fong and G. M. Seitz, Groups with a (B, N)-pair of rank 2. I, II, Invent. Math. 21 (1973). 1-57; 24 (1974), 191-239. MR 354858
30.
J. S. Frame, The classes and representations of the groups of 27 lines and 28 bitangents, Ann. Mat. Pura Appl. 32 (1951), 83-119. MR 47038
31.
J. S. Frame, The characters of the Weyl group E8, Computational Problems in Abstract Algebra (Proc. Conf. Oxford 1967), ed. J. Leich, Pergamon, Oxford, 1970, pp. 111-130. MR 269751
32.
H. Garland, p-adic curvature and the cohomology of discrete subgroups of p-adic groups, Ann. of Math. (2) 97 (1973), 375-423. MR 320180
33.
S. E. Gelfand, Representation of the full linear group over a finite field, Mat. Sb. 83 (125) (1970), 15-41. (Russian) MR 272916
34.
J. A. Green, The characters of the finite general linear groups, Trans. Amer. Math. Soc. 80 (1955), 402-447. MR 72878
35.
J. A. Green, On the Steinberg characters of finite Chevalley groups, Math. Z. 117 (1970), 272-288. MR 280612
36.
A. Grothendieck, Formule de Lefschetz et rationalité des functions - L, Sem. Bourbaki 279, Decembre 1964, Benjamin, New York. MR 212024
37.
Harish-Chandra, Eisenstein series over finite fields, Functional Analysis and Related Fields, Springer-Verlag, Berlin and New York, 1970, pp. 76-88. MR 457579
38.
P. Hoefsmit, Representations of Hecke algebras of finite groups with (B, N)-pairs of classical type, Ph.D. dissertation, Univ. of British Columbia, Vancouver, 1974.
39.
R. B. Howlett, On the degrees of Steinberg characters of Chevalley groups, Math. Z. 135 (1974), 125-135. MR 360781
40.
N. Iwahori, On the structure of the Hecke ring of a Chevalley group over a finite field, J. Fac. Sci. Univ. Tokyo Sect. IA 10 (1964), 215-236. MR 165016
41.
N. Kawanaka, A theorem on finite Chevalley groups, Osaka J. Math. 101 (1973), 1-13. MR 332948
42.
N. Kawanaka, Unipotent elements and characters of finite Chevalley groups, Osaka J. Math. (to appear). MR 384914
43.
D. Kazhdan, Proof of Springer's hypothesis, Israel J. Math. (to appear). MR 693352
44.
R. Kilmoyer, Some irreducible complex representations of a finite group with a BN-pair, Ph.D. dissertation, M.I.T., 1969.
45.
R. Kilmoyer, Principal series representations of finite Chevalley groups, J. Algebra (to appear). MR 487479
46.
T. Kondo, The characters of the Weyl group of type F4, J. Fac. Sci. Univ. Tokyo Sect. I, 11 (1965), 145-153. MR 185018
47.
B. Kostant, Groups over Z, Proc. Sympos. Pure Math., vol. 9, Amer. Math. Soc., Providence, R. I., 1966, pp. 90-98. MR 207713
48.
G. I. Lehrer, Adjoint groups, regular unipotent elements and discrete series characters, Trans. Amer. Math. Soc. 214 (1975), 249-260. MR 384915
49.
G. Lusztig, The discrete series representations of the general linear groups over a finite field, Ann. of Math. Studies, no. 81, Princeton Univ. Press, Princeton, N. J., 1974. MR 382419
50.
G. Lusztig, On the Green polynomials of classical groups, Proc. London Math. Soc. 33 (1976), 443-475. MR 424959
51.
G. Lusztig, Coxeter orbits and eigenspaces of Frobenius, Invent. Math. 28 (1975), 101-159. MR 453885
52.
G. Lusztig, On the finiteness of the number of unipotent classes, Invent. Math. 34 (1976), 201-213. MR 419635
53.
G. Lusztig, Irreducible representations of finite classical groups, Invent. Math. 43 (1977), 125-175. MR 463275
54.
G. Lusztig, Unipotent representations of a finite Chevalley group of type E8 (to appear).
55.
G. Lusztig, On the reflection representation of a finite Chevalley group (to appear).
56.
G. Lusztig, Representations of finite Chevalley groups, CBMS Regional Conf. Ser. in Math., no. 39, Amer. Math. Soc., Providence, R. I., 1978. MR 518617
57.
G. Lusztig and B. Srinivasan, The characters of the finite unitary groups, J. Algebra 49 (1977), 167-171. MR 453886
58.
H. Matsumoto, Générateurs et relations des groupes de Weyl generalise, C. R. Acad. Sci. Paris 258. MR 183818
59.
F. Richen, Modular representations of split (B, N)-pairs, Trans. Amer. Math. Soc. 140 (1969), 435-460. MR 242972
60.
G. M. Seitz, Flag transitive subgroups of Chevalley groups, Ann. of Math. (2) 97 (1973), 27-56. MR 340446
61.
L. Solomon, The Steinberg character of a finite group with a BN-pair, Theory of Finite Groups (ed. by R. Brauer and C. H. Sah), Benjamin, New York, 1969, pp. 213-221. MR 246951
62.
L. Solomon, On the affine group over a finite field, Representation Theory of Finite Groups and Related Topics, Proc. Sympos. Pure Math., vol. 21, Amer. Math. Soc., Providence, R. I., 1971. MR 318287
63.
L. Solomon, The affine group I. Bruhat decomposition, J. Algebra 20 (1972), 512-539. MR 306349
64.
T. A. Springer, Cusp forms for finite groups, and characters of special groups, parts C and D in Seminar on Algebraic Groups and Related Topics (ed. A. Borel) Lecture Notes in Math., vol. 131, Springer-Verlag, Berlin and New York, 1970. MR 263942
65.
T. A. Springer, On the characters of certain finite groups, Proc. Summer School, Group Representations, Budapest, 1971.
66.
T. A. Springer, Caractères de groupes de Chevalley finis, Sem. Bourbaki, no. 429, 1972/73.
67.
T. A. Springer, Relèvement de Brauer et représentations paraboliques de GL(F), Sem. Bourbaki, no. 441, 1973/74.
68.
T. A. Springer, Generalization of Green's polynomials, Proc. Sympos. Pure Math., vol. 21, Amer. Math. Soc., Providence, R. I., 1971, pp. 141-153. MR 327926
69.
T. A. Springer, Trigonometric sums, Green's functions of finite groups and representations of Weyl groups, Invent. Math. 36 (1976), 173-207. MR 442103
70.
T. A. Springer and R. Steinberg, Conjugacy classes, Part E in Seminar on Algebraic Groups and Related Topics, Lecture Notes in Math., vol. 131, Springer-Verlag, Berlin and New York, 1970. MR 268192
71.
B. Srinivasan, The characters of the finite symplectic group Sp(4, q), Trans. Amer. Math. Soc. 131 (1968), 488-525. MR 220845
72.
B. Srinivasan, On the Steinberg character of a finite simple group of Lie type, J. Austral. Math. Soc. 12 (1971), 1-14. MR 291317
73.
B. Srinivasan, Green polynomials of finite classical groups, Comm. Algebra 5 (1977), 1241-1258. MR 498889
74.
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. MR 43784
75.
B. Srinivasan, Prime power representations of finite linear groups. II, Canad. J. Math. 9 (1957), 347-351. MR 87659
76.
B. Srinivasan, Lectures on Chevalley groups, Yale University, 1967.
77.
B. Srinivasan, Endomorphisms of linear algebraic groups, Mem. Amer. Math. Soc. no. 80 (1968). MR 230728
78.
D. Surowski, Irreducible characters of BN-pairs of exceptional type, Ph.D. dissertation, Univ. of Arizona, 1975.
79.
D. Surowski, Representations of a subalgebra of the generic algebra corresponding to the Weyl group of type F4, Comm. Algebra 5 (1977), 873-888. MR 442104
80.
D. Surowski, Irreducible characters of BN-pairs of exceptional types, Trans. Amer. Math. Soc. (to appear). MR 502905
81.
J. Tits, Buildings of spherical type and finite BN-pairs, Lecture Notes in Math., vol. 386, Springer-Verlag, Berlin and New York, 1974. MR 470099
82.
A. Weil, Number of solutions of equations in finite fields, Bull. Amer. Math. Soc. 55 (1949), 497-508. MR 29393

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Additional Information:

DOI: 10.1090/S0273-0979-1979-14648-2
PII: S 0273-0979(1979)14648-2




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