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WOLFRAM|DEMONSTRATIONS PROJECT

2D Root Systems

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lattice type:
A
2
B
2
G
2
show reflected roots
A root system in
n
is a finite collection of spanning vectors (roots) closed under reflection with respect to planes perpendicular to roots. Any hyperplane in
n
divides roots in two sets—positive and negative roots. There are only three irreducible root systems in
2
, labeled
A
2
,
B
2
and
G
2
. Roots of different length are colored differently. Drag the locator to choose the reflection plane. Click on "show reflected roots" and note that the root system is closed under reflections about the line perpendicular to a root.
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