Weil's representations of the symplectic groups over finite fields

Hiroyuki YOSHIDA

doi:10.2969/jmsj/03120399

Hiroyuki YOSHIDA

著者情報

ジャーナルフリー

1979 年 31 巻 2 号 p. 399-426

DOI https://doi.org/10.2969/jmsj/03120399

詳細

Published: 1979 Received: 1978/05/15 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) J. S. Andrade, Représentations de Weil de GSp(4, F_q) associée à un espace quadratique de dimension 4 sur F_q, C. R. Acad. Sci. Paris, 278 (1974), 227-230.
2) J. S. Andrade, La représentations de Weil de GSp(4, F_q) et les représentations de Sp(4, F_q), C. R. Acad. Sci. Paris, 278 (1974), 321-324.
3) J. S. Andrade, Constructions géometrique de certaines series discretes, Lecture note in mathematics 597, 32-55, Springer, 1977.
4) P. Deligne and G. Lusztig, Representations of reductive groups over finite fields, Ann. of Math., 103 (1976), 103-161.
5) S. Gelbart, Holomorphic discrete series for the real symplectic group, Invent. Math., 19 (1973), 49-58.
6) R. Howe, Dual reductive pairs, to appear.
7) H. Jacquet and R. P. Langlands, Automorphic forms on GL(2), Lecture note in mathematics 114, Springer, 1970.
8) G. Lusztig, On the Green polynomials of classical groups, Proc. London Math. Soc., (3) 33 (1976), 443-475.
9) G. Lusztig, A note on counting nilpotent matrices of fixed rank, Bull. London Math. Soc., 8 (1976), 77-80.
10) J. Milnor, On isometries of inner product spaces, Invent, Math., 8 (1969), 83-97.
11) M. Saito, Représentations unitaires des groupes symplectique, J. Math. Soc. Japan, 24 (1972), 232-251.
12) G. Shimura, Arithmetic of unitary groups, Ann. of Math., 79 (1964), 369-409.
13) G. Shimura, Theta functions with complex multiplication, Duke Math. J., 43(1976), 673-696.
14) T. A. Springer and R. Steinberg, Conjugacy classes, Lecture note in mathematics 131, 167-266, Springer, 1970.
15) S. Tanaka, On irreducible unitary representations of some special linear groups of the second order, I, II, Osaka J. Math., 3 (1966), 217-227, 229-242.
16) S. Tanaka, Construction and classification of irreducible representations of special linear group of the second order over a finite field, Osaka J. Math., 4 (1967), 65-84.
17) A. Weil, Sur certains groupes d'opérateurs unitaires, Acta Math., 111 (1964), 143-211.

Right : [1] J. S. Andrade, Représentations de Weil de GSp(4, F_q) associée à un espace quadratique de dimension 4 sur F_q, C. R. Acad. Sci. Paris, 278 (1974), 227-230.
[2] J. S. Andrade, La représentations de Weil de GSp(4, F_q) et les représentations de Sp(4, F_q), C. R. Acad. Sci. Paris, 278 (1974), 321-324.
[3] J. S. Andrade, Constructions géometrique de certaines series discretes, Lecture note in mathematics 597, 32-55, Springer, 1977.
[4] P. Deligne and G. Lusztig, Representations of reductive groups over finite fields, Ann. of Math., 103 (1976), 103-161.
[5] S. Gelbart, Holomorphic discrete series for the real symplectic group, Invent. Math., 19 (1973), 49-58.
[6] R. Howe, Dual reductive pairs, to appear.
[7] H. Jacquet and R. P. Langlands, Automorphic forms on GL(2), Lecture note in mathematics 114, Springer, 1970.
[8] G. Lusztig, On the Green polynomials of classical groups, Proc. London Math. Soc., (3) 33 (1976), 443-475.
[9] G. Lusztig, A note on counting nilpotent matrices of fixed rank, Bull. London Math. Soc., 8 (1976), 77-80.
[10] J. Milnor, On isometries of inner product spaces, Invent, Math., 8 (1969), 83-97.
[11] M. Saito, Représentations unitaires des groupes symplectique, J. Math. Soc. Japan, 24 (1972), 232-251.
[12] G. Shimura, Arithmetic of unitary groups, Ann. of Math., 79 (1964), 369-409.
[13] G. Shimura, Theta functions with complex multiplication, Duke Math. J., 43 (1976), 673-696.
[14] T. A. Springer and R. Steinberg, Conjugacy classes, Lecture note in mathematics 131, 167-266, Springer, 1970.
[15] S. Tanaka, On irreducible unitary representations of some special linear groups of the second order, I, II, Osaka J. Math., 3 (1966), 217-227, 229-242.
[16] S. Tanaka, Construction and classification of irreducible representations of special linear group of the second order over a finite field, Osaka J. Math., 4 (1967), 65-84.
[17] A. Weil, Sur certains groupes d'opérateurs unitaires, Acta Math., 111 (1964), 143-211.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

責任著者(Corresponding author)

訂正情報

J-STAGEへの登録はこちら（無料）