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Irreducible representations of finite classical groups. (English) Zbl 0372.20033

20G40Linear algebraic groups over finite fields
20G05Representation theory of linear algebraic groups
Full Text: DOI EuDML
[1] Andrews, G.E.: Partitions,q-functions and the Lusztig-Macdonald-Wall conjectures, Inventiones math.41, 91-102 (1977) · Zbl 0354.20006 · doi:10.1007/BF01390165
[2] Benson, C.T., Gay, D.A.: On dimension functions of the generic algebra of typeD n , J. of Algebra,45, 435-438 (1977) · Zbl 0371.20036 · doi:10.1016/0021-8693(77)90335-0
[3] Bourbaki, N.: Groupes et algèbres de Lie, Ch. 4,5 et 6. Paris: Hermann 1968 · Zbl 0186.33001
[4] Deligne, P., Lusztig, G.: Representations of reductive groups over finite fields. Ann. of Math.103, 103-161 (1976) · Zbl 0336.20029 · doi:10.2307/1971021
[5] Dye, R.: The simple groupFH (8, 2) of order 212{$\cdot$}35{$\cdot$}52{$\cdot$}7 and the associated geometry of triality. Proc. London Math. Soc. (3)18, 521-562 (1968) · Zbl 0159.31104 · doi:10.1112/plms/s3-18.3.521
[6] Enomoto, H.: The characters of the finite symplectic groupSp(4,q),q=2 f . Osaka J. Math.9, 75-94 (1972) · Zbl 0254.20005
[7] Frame, J.S., Rudvalis, A.: Characters of symplectic groups overF 2, Finite groups ’72. Proc. Gainesville Conf. p. 41-54. North Holland, Amsterdam 1973 · Zbl 0256.20008
[8] Harish-Chandra: Eisenstein series over finite fields. Funct. Analysis and Related Fields (ed. F.E. Browder). Berlin-Heidelberg-New York: Springer 1970 · Zbl 0226.20049
[9] Hardy, G.H., Wright, E.M.: The theory of numbers. Oxford: Clarendon Press 1971 · Zbl 0020.29201
[10] Hoefsmit, P.N.: Representations of Hecke algebras of finite groups withBN pairs of classical type, Thesis, Univ. of British Columbia, Vancouver 1974
[11] Kilmoyer, R.: Principal series representations of finite Chevalley groups (preprint, Clark University) · Zbl 0389.20008
[12] Langlands, R. P.: On the classification of irreducible representations of real algebraic groups, preprint, Institute for Advanced Study · Zbl 0741.22009
[13] Lusztig, G.: Classification des représentations irréductibles des groupes classiques finis. c. r. Acad. Sci. Paris. Sér. A,284, 473-475 (28 Fév. 1977) · Zbl 0352.20038
[14] Lusztig, G.: Coxeter orbits and eigenspaces of Frobenius, Inventiones math.38, 101-159 (1976) · Zbl 0366.20031 · doi:10.1007/BF01408569
[15] Lusztig, G.: On the finiteness of the number of unipotent classes, Inventiones math.34, 201-213 (1976) · Zbl 0371.20039 · doi:10.1007/BF01403067
[16] Lusztig, G., Srinivasan, B.: The characters of the finite unitary groups (to appear in the J. of Algebra) · Zbl 0384.20008
[17] Spaltenstein, N.: Sous-groupes de Borel contenant un unipotent donné (preprint, University of Warwick)
[18] Srinivasan, B.: The characters of the finite symplectic groupSp(4,q), Trans. Amer. math. Soc.131, 488-525 (1968) · Zbl 0213.30401
[19] Steinberg, R.: A geometric approach to the representations of the full linear group over a Galois field, Trans. Amer. math. Soc.71, 274-282 (1951) · Zbl 0045.30201 · doi:10.1090/S0002-9947-1951-0043784-0
[20] Wall, G. E.: On the conjugacy classes in the unitary, symplectic and orthogonal groups, J. Austral. math. Soc.3, 1-62 (1963) · Zbl 0122.28102 · doi:10.1017/S1446788700027622