Document Zbl 0389.20037

A specialization theorem for certain Weyl group representations and an application to the Green polynomials of unitary groups. (English) Zbl 0389.20037

Invent. Math. 41, 113-127 (1977).

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MSC:

20G40	Linear algebraic groups over finite fields
20G15	Linear algebraic groups over arbitrary fields
20G05	Representation theory for linear algebraic groups
20E10	Quasivarieties and varieties of groups
20J05	Homological methods in group theory

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References:

[1]	Artin, M., Grothendieck, A., Verdier, J.L.: Théorie des topos et cohomologie étale des schémas, SGA 4, Lecture Notes in Math. 269, 270, 305. Berlin-Heidelberg-New York: Springer 1972/73
[2]	Deligne, P.: Cohomologie étale, SGA 41/2, Lecture Notes in Math. 569. Berlin-Heidelberg-New York: Springer 1977 · Zbl 0345.00010
[3]	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
[4]	Ennola, V.: On the characters of the finite unitary groups. Ann. Acad. Sci. Fenn.323, 1-35 (1963) · Zbl 0109.26001
[5]	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
[6]	Kawanaka, N.: On the irreducible characters of the finite unitary groups. To appear · Zbl 0371.20017
[7]	Kazhdan, D.: Proof of Springer’s hypothesis. To appear · Zbl 0391.22006
[8]	Lusztig, G.: On the Green polynomials of classical groups. Proc. London math. Soc.33, 443-475 (1976) · Zbl 0371.20037 · doi:10.1112/plms/s3-33.3.443
[9]	Lusztig, G., Srinivasan, B.: The characters of the finite unitary groups. To appear · Zbl 0384.20008
[10]	Macdonald, I.G.: Some irreducible representations of Weyl groups. Bull. London math. Soc.4, 148-150 (1972) · Zbl 0251.20043 · doi:10.1112/blms/4.2.148
[11]	Mazur, B.: Eigenvalues of Frobenius acting on algebraic varieties over finite fields. In: Proceedings of Symposia in Pure Mathematics Vol.29, pp. 231-261, Amer. math. Soc. 1975 · Zbl 0306.14011
[12]	Spaltenstein, N.: The fixed point set of a unipotent transformation on the flag manifold. Proc. Kon. Ak. v. Wet.79(5), 452-456 (1976) · Zbl 0343.20029
[13]	Springer, T.A.: Trigonometric sums, Green functions of finite groups and representations of Weyl groups. Inventiones math.36, 173-207 (1976) · Zbl 0374.20054 · doi:10.1007/BF01390009
[14]	Springer, T.A.: Generalization of Green’s polynomials. In: Proceedings of Symposia in Pure Mathematics Vol.21, pp. 149-153, Amer. math. Soc. 1971 · Zbl 0247.20049
[15]	Steinberg, R.: On the desingularization of the unipotent variety. Inventiones math.36, 209-224 (1976) · Zbl 0352.20035 · doi:10.1007/BF01390010

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