## Journal of the Mathematical Society of Japan

### Fundamental Hermite constants of linear algebraic groups

Takao WATANABE

#### Abstract

Let $G$ be a connected reductive algebraic group defined over a global field $k$ and $Q$ a maximal $k$-parabolic subgroup of $G$. The constant $\gamma(G,Q,k)$ attached to $(G,Q)$ is defined as an analogue of Hermite's constant. This constant depends only on $G,$$Q$ and $k$ in contrast to the previous definition of generalized Hermite constants ([W1]). Some functorial properties of $\gamma(G,Q,k)$ are proved. In the case that $k$ is a function field of one variable over a finite field, $\gamma(GL_{n},Q,k)$ is computed.

#### Article information

Source
J. Math. Soc. Japan, Volume 55, Number 4 (2003), 1061-1080.

Dates
First available in Project Euclid: 3 October 2007

https://projecteuclid.org/euclid.jmsj/1191418764

Digital Object Identifier
doi:10.2969/jmsj/1191418764

Mathematical Reviews number (MathSciNet)
MR2003760

Zentralblatt MATH identifier
1103.11033

#### Citation

WATANABE, Takao. Fundamental Hermite constants of linear algebraic groups. J. Math. Soc. Japan 55 (2003), no. 4, 1061--1080. doi:10.2969/jmsj/1191418764. https://projecteuclid.org/euclid.jmsj/1191418764