Abstract
Let G be a connected reductive group defined over the finite field 픽 q , and let
be its Lie algebra. Let F: G → G be the corresponding Frobenius endomorphism and write also
for the induced Frobenius map on
. We are concerned here with the space
of Ad G F—invariant functions:
. Let
be the nilpotent variety of
.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
F. Digne, G.I. Lehrer and J. Michel, The characters of the group of rational points of a reductive group with non-connected centre, J. reine angew.Math. 425(1992), 155–192.
F. Digne and J. Michel, Representations of reductive groups over finite fields, Cambridge D.P., Cambridge (1991).
J.A. Green, The characters of the finite general linear groups, Trans. A.M.S.80(1955), 402–447.
N. Kawanaka, Fourier transforms of nilpotently supported invariant functions on a finite simple Lie algebra, Invent. Math. 69(1982), 411–435.
N. Kawanaka, Generalised Gelfand-Graev representations of exceptional simple algebraic groups over a finite field, Invent. Math. 84(1986), 575–616.
S.V. Keny, Existence of regular nilpotent elements in the Lie algebra of a simple algebraic group in bad characteristics, J. Algebra, 108(1987), 194–201.
B. Kostant, Lie group representations on polynomial rings, Amer. J. Math. 85(1963), 327–404.
G.I. Lehrer, The space of invariant functions on a finite Lie algebra, Trans. A.M.S. 348(1996) 31–50.
G.I. Lehrer, On the values of characters of semisimple groups over finite fields, Osaka J. Math.15(1978), 77–99.
G.I. Lehrer, Rational tori, semisimple orbits and the topology of hyperplane complements, Comment. Math. Helvetici 67(1992), 226–251.
G. Lusztig, A unipotent support for irreducible representations, Adv. Math. 94(1992), 139–179.
G. Lusztig and N. Spaltenstein, Induced unipotent classes, J. Lond. Math. Soc. 19(1979),41–52.
I.G. MacDonald, Symmetric functions and Hall polynomials, Clarendon Press, Oxford 1979.
T. Shoji, Geometry of orbits and Springer correspondence, Soc. Math. France Asierisque 168(1988), 61–140.
T.A. Springer, Trigonometric sums, Green functions of finite groups and representations of Weyl groups, Invent. Math. 36 (1976), 173–207.
T.A. Springer, Generalisation of Green’s polynomials, Proc. Symp. Pure Math. A.M.S. 21(1972), 159–153.
T.A. Springer and R. Steinberg, Conjugacy classes, in Seminar on Algebraic Groups and Related Finite Groups, Lecture Notes in Math. 131, Springer Verlag (1970), 167–266.
R. Steinberg, Regular elements in algebraic groups, Publ. Math. I.H.E.S. 25(1965),49–80.
R. Steinberg, Lectures on Chevalley groups, Yale University (1967).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Birkhäuser Boston
About this chapter
Cite this chapter
Lehrer, G.I. (1997). Fourier transforms, Nilpotent Orbits, Hall Polynomials and Green Functions. In: Cabanes, M. (eds) Finite Reductive Groups: Related Structures and Representations. Progress in Mathematics, vol 141. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4124-9_11
Download citation
DOI: https://doi.org/10.1007/978-1-4612-4124-9_11
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8664-6
Online ISBN: 978-1-4612-4124-9
eBook Packages: Springer Book Archive