Coxeter groups

Applications for exploring Coxeter groups and their associated structures. These apps are powered by a TypeScript port of PyCox by Meinolf Geck.

• Coxeter Group Explorer — inspect the root system, Cartan and Coxeter matrices, length distribution, conjugacy classes, parabolic and reflection subgroups, the word inspector, character tables, and the Hecke character table for any Coxeter group of classical or exceptional type.
• Bruhat Order — visualize the Bruhat order of any Coxeter group.
• Kazhdan–Lusztig Polynomials — compute Kazhdan–Lusztig polynomials, left/right/two-sided cells, and Duflo involutions for any Coxeter group.
• Longest Weyl Parabolic — compute the longest elements of a Weyl group and a parabolic subgroup, displayed as matrices in the standard model for types A, B, C, D.

📄️Coxeter Group Explorer

Inspect the root system, matrices, length distribution, conjugacy classes, subgroups, and character tables for any Coxeter group

📄️Kazhdan–Lusztig Polynomials

Compute Kazhdan–Lusztig polynomials, cells, and Duflo involutions for Coxeter groups

📄️Bruhat Order

Visualize the Bruhat order of any Coxeter group

📄️Longest Weyl Parabolic

Compute the longest elements of a Weyl group and a parabolic subgroup, and display them as matrices in the standard group model for types A, B, C, D