# Gauss sum for the adjoint representation of $G{L}_{n}\left(q\right)$ and $S{L}_{n}\left(q\right)$

Yeon-Kwan Jeong; In-Sok Lee; Hyekyoung Oh; Kyung-Hwan Park

Acta Arithmetica (2000)

- Volume: 95, Issue: 1, page 1-16
- ISSN: 0065-1036

## Access Full Article

top## How to cite

topJeong, Yeon-Kwan, et al. "Gauss sum for the adjoint representation of $GL_{n}(q)$ and $SL_{n}(q)$." Acta Arithmetica 95.1 (2000): 1-16. <http://eudml.org/doc/207439>.

@article{Jeong2000,

author = {Jeong, Yeon-Kwan, Lee, In-Sok, Oh, Hyekyoung, Park, Kyung-Hwan},

journal = {Acta Arithmetica},

keywords = {adjoint representation; $GL_\{n\}(q)$; $SL_\{n\}(q)$; Gauss sum; $PGL_\{n\}(q)$; GL; PGL; SL; multiplicative character; finite group of Lie type; character sums},

language = {eng},

number = {1},

pages = {1-16},

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

url = {http://eudml.org/doc/207439},

volume = {95},

year = {2000},

}

TY - JOUR

AU - Jeong, Yeon-Kwan

AU - Lee, In-Sok

AU - Oh, Hyekyoung

AU - Park, Kyung-Hwan

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

JO - Acta Arithmetica

PY - 2000

VL - 95

IS - 1

SP - 1

EP - 16

LA - eng

KW - adjoint representation; $GL_{n}(q)$; $SL_{n}(q)$; Gauss sum; $PGL_{n}(q)$; GL; PGL; SL; multiplicative character; finite group of Lie type; character sums

UR - http://eudml.org/doc/207439

ER -

## References

top- [1] A. Borel, Linear Algebraic Groups, Benjamin, New York, 1969. Zbl0186.33201
- [2] R. W. Carter, Finite Groups of Lie Type; Conjugacy Classes and Complex Characters, Wiley, New York, 1985. Zbl0567.20023
- [3] W. Fulton and J. Harris, Representation Theory, Springer, New York, 1991. Zbl0744.22001
- [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. Zbl1036.11528
- [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. Zbl1036.11527
- [8] D. S. Kim, Gauss sums for $O(2n+1,q)$, Finite Fields Appl. 4 (1998), 62-86. Zbl0937.11058
- [9] D. S. Kim, Gauss sum for $U(2n,{q}^{2})$, Glasgow Math. J. 40 (1998), 79-95. Zbl0915.11061
- [10] D. S. Kim, Gauss sums for symplectic groups over a finite field, Monatsh. Math., to appear. Zbl1036.11529
- [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 ${G}_{2}\left(q\right)$, Bull. Korean Math. Soc. 34 (1997), 305-315. Zbl0891.11059
- [14] K.-H. Park, Gauss sum for representations of $G{L}_{n}\left(q\right)$ and $S{L}_{n}\left(q\right)$, thesis, Seoul National University, 1998.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.