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Structure Theory

Pick a group once with the shared picker below, then either run each mini app individually or use Run all mini apps to compute every structure-theory section on this page at once. Each mini app links directly to its atlas documentation page.

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Atlas expression

Mode: Real groupFamily: SLₙ(ℂ)Selection: SU(1,0)

Type A, simply connected.

Compact form.

SU(1,0)

Cartan subgroups​

Classify the conjugacy classes of Cartan subgroups for the selected real form. See the atlas docs on Cartan classes.

Atlas docs ↗
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Results

Choose a group and run the atlas command to see structured results.

K-orbits on G/B​

List the orbits of K on the flag variety G/B (the KGB structure). See the atlas docs on K-orbits on G/B.

Atlas docs ↗
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Results

Choose a group and run the atlas command to see structured results.

Real Weyl group​

Compute the real Weyl group attached to the selected real form. See the atlas docs on real forms.

Atlas docs ↗
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Results

Choose a group and run the atlas command to see structured results.

Component group​

Compute the component group of the real form. See the atlas docs on components/rank.

Atlas docs ↗
Run:

Results

Choose a group and run the atlas command to see structured results.

Strong real forms​

List the strong real forms in the square class of the selected real form. See the atlas docs on square classes.

Atlas docs ↗
Run:

Results

Choose a group and run the atlas command to see structured results.