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Induced cuspidal representations and generalised Hecke rings. (English) Zbl 0435.20023


MSC:

20G05 Representation theory for linear algebraic groups
20G40 Linear algebraic groups over finite fields

References:

[1] Benson, C.T., Curtis, C.W.: On the degrees and rationality of certain characters of finite Chevalley groups. Trans. Amer. Math. Soc.165, 251-274 (1972) · Zbl 0246.20008 · doi:10.1090/S0002-9947-1972-0304473-1
[2] Borel, A., Tits, J.: Groupes réductifs. Publ. Math. I.H.E.S.27, 55-152 (1965) · Zbl 0145.17402
[3] Bourbaki, N.: Groupes et algèbres de Lie, Chap. IV, V, VI. Paris: Hermann 1968
[4] Curtis, C.W., Fossum, T.V.: On centralizer rings and characters of representations of finite groups. Math. Zeit.107, 402-406 (1968) · Zbl 0185.06801 · doi:10.1007/BF01110070
[5] Curtis, C.W., Iwahori, N., Kilmoyer, R.: Hecke algebras and characters of parabolic type of finite groups with (B, N) pairs. Publ. Math. I.H.E.S.40, 81-116 (1972) · Zbl 0254.20004
[6] Curtis, C.W., Reiner, I.: Representation theory of finite groups and associative algebras. Interscience 1962 · Zbl 0131.25601
[7] 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
[8] Green, J.A.: The characters of the finite general linear groups. Trans. Amer. Math. Soc.80, 402-447 (1955) · Zbl 0068.25605 · doi:10.1090/S0002-9947-1955-0072878-2
[9] Harish-Chandra: Eisenstein series over finite fields, in functional analysis and related fields, Stone anniversary volume (F.E. Browder, ed.), pp. 76-88. Berlin Heidelberg New York: Springer-Verlag 1970 · Zbl 0226.20049
[10] Hoefsmit, P.: Representations of Hecke algebras of finite groups with (B, N) pairs of classical type. Ph.D. Dissertation, University of British Columbia, Vancouver, B.C., 1974
[11] Howlett, R.: Normalizers of parabolic subgroups of reflection groups. Proc. Lond. Math. Soc. in press (1980) · Zbl 0427.20040
[12] Howlett, R., Kilmoyer, R.W.: Principal series representations of finite groups withBN-pairs. In press (1980) · Zbl 0438.20029
[13] Kilmoyer, R.W.: Principal series representations of finite Chevalley groups. J. of Alg.51, 300-319 (1978) · Zbl 0389.20008 · doi:10.1016/0021-8693(78)90149-7
[14] Knapp, A.W.: Determination of intertwining operators. In: Proc. Symp. Pure Math. A.M.S. XXVI, 263-268 (1973) · Zbl 0288.22015
[15] Knapp, A.W.: Weyl group of a cuspidal parabolic. Ann. Scient. Ec. Norm. Sup. 275-294 (1975) · Zbl 0305.22010
[16] Knapp, A.W., Zuckermann: Normalizing factors, tempered representations andL-groups. In: Proc. Symp. Pure Math. XXXII Part i, (1979) · Zbl 0414.22017
[17] Lehrer, G.I.: The characters of the finite special linear groups. J. of Alg.26, 564-583 (1973) · Zbl 0265.20037 · doi:10.1016/0021-8693(73)90015-X
[18] Lehrer, G.I.: Adjoint groups regular unipotent elements and discrete series characters. Trans. Amer. Math. Soc.214, 249-260 (1975) · Zbl 0345.20047 · doi:10.1090/S0002-9947-1975-0384915-9
[19] Lusztig, G.: Coxeter orbits and eigenspaces of Frobenius. Inv. Math.38, 101-159 (1976) · Zbl 0366.20031 · doi:10.1007/BF01408569
[20] Lusztig, G.: Irreducible representations of finite classical groups. Inv. Math.43, 125-175 (1977) · Zbl 0372.20033 · doi:10.1007/BF01390002
[21] Richen, F.: Modular representations of split (B, N) pairs. Trans. Amer. Math. Soc.140, 435-460 (1969) · Zbl 0181.03801
[22] Springer, T.A.: Cusp forms for finite groups, in Lecture Notes in Mathematics 131, pp. 97-120. Springer-Verlag (1968)
[23] Springer, T.A.: On the characters of certain finite groups. In: ?Lie groups and their representations?, Budapest Summer School on Group Representations (I.M. Geldfand, ed.), pp. 621-644 (1971)
[24] Springer, T.A.: Caractères de groupes de Chevalley finis, sém. Bourbaki no. 429. In: Springer Lecture Notes in Mathematics 383, 227 (1974)
[25] Steinberg, R.: Lectures on Chevalley groups. Yale Lecture Notes, New Haven, Conn. 1967 · Zbl 0164.34302
[26] Tits, J.: Normalisateurs de tores, I. Groupes de Coxeter étendus. J. of Alg.4, 96-116 (1966) · Zbl 0145.24703 · doi:10.1016/0021-8693(66)90053-6
[27] Yokonuma, T.: Sur le commutant d’une représentation d’un group de Chevalley fini II. J. Fac. Sci. Univ. Tokyo, Sect I16, 65-81 (1969) · Zbl 0239.20052
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