Gauss sum for the adjoint representation of $GL_{n}(q)$ and $SL_{n}(q)$

• Autorzy: Yeon-Kwan Jeong , In-Sok Lee , Hyekyoung Oh , Kyung-Hwan Park
• Języki publikacji: EN

Słowa kluczowe

EN

adjoint representation; $GL_{n}(q)$; $SL_{n}(q)$; Gauss sum; $PGL_{n}(q)$

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2000
• Tom: 95
• Numer: 1
• Strony: 1-16

Daty

wydano

2000

otrzymano

1998-08-25

poprawiono

2000-03-06

Twórcy

autor

Yeon-Kwan Jeong

• Department of Mathematics, Seoul National University, Seoul 151-742, Korea

autor

In-Sok Lee

• Department of Mathematics, Seoul National University, Seoul 151-742, Korea

autor

Hyekyoung Oh

• Department of Mathematics, Seoul National University, Seoul 151-742, Korea

autor

Kyung-Hwan Park

• Department of Mathematics, Seoul National University, Seoul 151-742, Korea

Bibliografia

• [1] A. Borel, Linear Algebraic Groups, Benjamin, New York, 1969.
• [2] R. W. Carter, Finite Groups of Lie Type; Conjugacy Classes and Complex Characters, Wiley, New York, 1985.
• [3] W. Fulton and J. Harris, Representation Theory, Springer, New York, 1991.
• [4] J. E. Humphreys, Linear Algebraic Groups, Grad. Texts in Math. 21, Springer, 1975.
• [5] D. S. Kim, Gauss sums for general and special linear groups over a finite field, Arch. Math. (Basel) 69 (1997), 297-304.
• [6] D. S. Kim, Gauss sums for $O^-(2n,q)$, Acta Arith. 80 (1997), 343-365.
• [7] D. S. Kim, Gauss sum for $U(2n+1,q^2)$, J. Korean Math. Soc. 34 (1997), 871-894.
• [8] D. S. Kim, Gauss sums for $O(2n+1,q)$, Finite Fields Appl. 4 (1998), 62-86.
• [9] D. S. Kim, Gauss sum for $U(2n,q^2)$, Glasgow Math. J. 40 (1998), 79-95.
• [10] D. S. Kim, Gauss sums for symplectic groups over a finite field, Monatsh. Math., to appear.
• [11] D. S. Kim and I.-S. Lee, Gauss sums for $O^+(2n,q)$, Acta Arith. 78 (1996), 75-89.
• [12] D. S. Kim and Y. H. Park, Gauss sums for orthogonal groups over a finite field of characteristic two, ibid. 82 (1997), 331-357.
• [13] I.-S. Lee and K. H. Park, Gauss sums for $G_{2}(q)$, Bull. Korean Math. Soc. 34 (1997), 305-315.
• [14] K.-H. Park, Gauss sum for representations of $GL_{n}(q)$ and $SL_{n}(q)$, thesis, Seoul National University, 1998.