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Generalized Green functions and unipotent classes for finite reductive groups. II. (English) Zbl 1133.20036
Summary: This paper is concerned with the problem of the determination of unknown scalars involved in the algorithm of computing the generalized Green functions of reductive groups $$G$$ over a finite field. In the previous paper [Nagoya Math. J. 184, 155-198 (2006; Zbl 1128.20033)], we have treated the case where $$G=\text{SL}_n$$. In this paper, we determine the scalars in the case where $$G$$ is a classical group $$\text{Sp}_{2n}$$ or $$\text{SO}_N$$ for arbitrary characteristic.

##### MSC:
 20G05 Representation theory for linear algebraic groups 20G40 Linear algebraic groups over finite fields
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##### References:
 [1] J. Dieudonné, La Géométrie des Groupes Classiques, Springer-Verlag, 1971. [2] G. Lusztig, Intersection cohomology complexes on a reductive group , Invent. Math., 75 (1984), 205-272. · Zbl 0547.20032 [3] G. Lusztig, Character sheaves, I , Adv. in Math., 56 (1985), 193-237, II , Adv. in Math., 57 (1985), 226-265, III , Adv. in Math., 57 (1985), 266-315, IV , Adv. in Math., 59 (1986), 1-63, \emphV, Adv. in Math., 61 (1986), 103-155. · Zbl 0586.20018 [4] G. Lusztig and N. Spaltenstein, On the generalized Springer correspondence for classical groups , Advanced Studies in Pure Math. Vol. 6 (1985), pp. 289-316. · Zbl 0579.20035 [5] T. Shoji, On the Green polynomials of classical groups , Invent. Math., 74 (1983), 237-267. · Zbl 0525.20027 [6] T. Shoji, Generalized Green functions and unipotent classes for finite reductive groups, I , Nagoya Math. J., 184 (2006), 155-198. · Zbl 1128.20033 [7] N. Spaltenstein, Classes Unipotentes et Sous-groupes de Borel, Lecture Note in Math. 946 , Springer-Verlag, 1982. · Zbl 0486.20025 [8] N. Spaltenstein, On the generalized Springer correspondence for exceptional groups , Advanced Studies in Pure Math. Vol. 6 (1985), pp. 317-338. · Zbl 0574.20029 [9] T. A. Springer and R. Steinberg, Conjugacy classes , Seminar on Algebraic Groups and Related Finite Groups, Lect. Note in Math. 131 , Springer-Verlag (1970), pp. 167-266.
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