Wavefronts Playground

An interactive playground for computing and visualizing the associated varieties and arithmetic wavefronts of discrete series representations of real classical groups. Based on the algorithms from:

Reference: Liu, D., Luo, Z., Ma, J.-J., & Zhang, L. Associated variety coincides with arithmetic wavefront for real classical groups.
This playground implements the algorithms from Sections 4 & 5.

🔄 Associated Variety (AV)

Computed from Harish-Chandra parameters (δ-sequence)

📈 Arithmetic Wavefront

Computed from Langlands parameters (χ-sequence)

HC Parameter & Associated Variety

ℹ️

Harish-Chandra Parameter: Auxiliary Sign (Type B only):

Associated Variety

➡️ Select Lie type and enter parameters

Then click "Generate Wavefronts"

Configuration

Lie Type

Aₙ Unitary Bₙ Odd Orthogonal Cₙ Symplectic Dₙ Even Orthogonal

Langlands Parameter & Arithmetic Wavefront

ℹ️

Langlands Parameter: Auxiliary Sign (Type B only):

Arithmetic Wavefront

💡 Click rows for details

⬅️ Select Lie type and enter parameters

Then click "Generate Wavefronts"