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2015 Reflection groups of the quadratic form $-px_0^2+x_1^2+\dotsb+x_n^2$ with $p$ prime
Alice Mark
Publ. Mat. 59(2): 353-372 (2015).


We present the classification of reflective quadratic forms $-px_0^2+x_1^2+\dotsb+x_n^2$ for $p$ prime. We show that for $p = 5$, it is reflective for $2\leq n\leq 8$, for $p = 7\text{ and }17$ it is reflective for $n = 2\text{ and }3$, for $p=11$ it is reflective for $p=2$, $3,\text{ and } 4$, and it is not reflective for higher values of $n$. We also show that it is non-reflective for $n > 2$ when $p = 13$, $19,\text{ and }23$. This completes the classification of these forms with $p$ prime.


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Alice Mark. "Reflection groups of the quadratic form $-px_0^2+x_1^2+\dotsb+x_n^2$ with $p$ prime." Publ. Mat. 59 (2) 353 - 372, 2015.


Published: 2015
First available in Project Euclid: 30 July 2015

zbMATH: 1330.20061
MathSciNet: MR3374612

Primary: 20F55
Secondary: 22E40

Keywords: Coxeter groups , reflection groups

Rights: Copyright © 2015 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.59 • No. 2 • 2015
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