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Unipotent characters of the symplectic and odd orthogonal groups over a finite field. (English) Zbl 0477.20023


MSC:

20G05 Representation theory for linear algebraic groups
20C15 Ordinary representations and characters
20G40 Linear algebraic groups over finite fields
20G10 Cohomology theory for linear algebraic groups
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References:

[1] Alvis, D.: The duality operation in the character ring of a finite Chevalley group. Bull. Amer. Math. Soc.1, 907-911 (1979) · Zbl 0485.20029
[2] Asai, T.: On the zeta functions of the varietiesX(w) of the split classical groups and the unitary groups. Preprint · Zbl 0515.20026
[3] Benson, C.T., Curtis, C.W.: On the degrees and rationality of certain characters of finite Chevalley groups. Trans. Amer. Math. Soc.165, 251-273 (1972) and202, 405-406 (1975) · Zbl 0246.20008
[4] Deligne, P.: Letter to D. Kazhdan and G. Lusztig, 20 April 1979
[5] Deligne, P., Lusztig, G.: Representations of reductive groups over finite fields. Ann. Math.103, 103-161 (1976) · Zbl 0336.20029
[6] Green, J.A.: On the Steinberg characters of finite Chevalley groups. Math. Z.,117, 272-288 (1970) · Zbl 0219.20003
[7] Kawanaka, N.: On the lifting of the irreducible characters of the finite classical groups. To appear in J. Fac. Sci. Univ. Tokyo · Zbl 0353.20031
[8] Kazhdan, D., Lusztig, G.: Representations of Coxeter groups and Hecke algebras. Invent. Math.53, 165-184 (1979) · Zbl 0499.20035
[9] Kazhdan, D., Lusztig, G.: Schubert varieties and Poincaré duality. Proc. Symp. in Pure Math. A.M.S.36, (1980) · Zbl 0461.14015
[10] Lusztig, G.: Irreducible representations of finite classical groups. Invent. Math.43, 125-175 (1977) · Zbl 0372.20033
[11] Lusztig, G.: Representations of finite Chevalley groups. C.B.M.S. Regional Conference series in Mathematics, Nr. 39, A.M.S., 1978 · Zbl 0418.20037
[12] Lusztig, G.: A class of irreducible representations of a Weyl group. Proc. Nederl. Akad, Series A,82, 323-335 (1979) · Zbl 0435.20021
[13] Lusztig, G.: On a theorem of Benson and Curtis. J. of Algebra, in press (1981) · Zbl 0465.20042
[14] Macdonald, I.G.: Symmetric functions and Hall polynomials. Oxford: Clarendon Press 1979 · Zbl 0487.20007
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