GKM Viewer

Interactive 3D viewers of the GKM (moment) graph of the affine Grassmannian for the rank-2 root systems A2, B2, G2. Vertices are T-fixed points (lattice points lifted onto the energy paraboloid, colored by energy E = |v|²); edges are the GKM / T-stable curves.

Controls

• Drag to rotate · scroll to zoom · right-drag to pan
• Click a vertex: cycles select → ▲ flow-up → ▼ flow-down → clear (shows simple-root coordinates and the Morse/flow cells)
• Click an edge: shows its edge volume vol = …

Files — open index.html (tabbed A2/B2/G2), or any of a2.html / b2.html / g2.html directly. Each viewer is fully self-contained (three.js embedded) and works offline.

Built from momentmap.nb (Hausel group).

Acknowledgement

Based on a note of Miguel González, Note on torus actions on affine Grassmannians — the GKM-graph conventions (vertices and one-dimensional orbits / edges) and the edge-volume formula that this viewer displays. Clicking an edge shows k·B(β∨,β∨) = |d|²/k, i.e. twice the symplectic ℙ¹ volume (k/2)·B(β∨,β∨) derived in that note (which in turn uses Godinho–von Heymann–Sabatini, 12, 24 and beyond, Adv. Math. 319 (2017)).