English

This interactive tool is a companion application for the article Weyl Groups and the Modified Kostant Game. It lets you explore the Kostant game and its modified version directly in your browser, with no installation required.

The game is played on a weighted directed graph whose nodes represent simple roots αᵢ of a root system. Each node carries a number of chips, and at each step a sad node — one whose chip count is less than half the weighted sum of its neighbors' chips — can be reflected, updating its count according to the formula cᵢ → −cᵢ + Σ nᵢⱼ cⱼ. The game ends when no sad nodes remain.

The modified version introduces always-happy special nodes (αᵢ') that are permanently fixed at 1 chip and always considered happy, allowing the study of boundary conditions analogous to affine Dynkin diagrams.

Features: build arbitrary graphs with simple or weighted directed edges, add special nodes, initialize the game from any node, step through reflections manually or run the full game automatically, and delete nodes or edges at any time during construction.

You are invited to create your own graphs and help the sad nodes!