Weyl Groups and the Modified Kostant Game
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917483495030784 |
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| author | Castro, Alexander Caviedes Cortés-Cruz, Juan Sebastián |
| author_facet | Castro, Alexander Caviedes Cortés-Cruz, Juan Sebastián |
| contents | This paper presents a generalization of the Kostant game, a combinatorial framework originally for generating positive roots in Lie algebras. By introducing an arbitrary multi-vertex modification, we prove that the resulting game configurations naturally biject with the minimal length representatives of parabolic quotients W/W_J. This yields a dynamical and algorithmic perspective on reduced words. Finally, we apply this framework to derive a novel root counting identity, formalize the Coxeter-theoretic foundation for combinatorial approaches to the Mukai conjecture, establish the regularity of reduced word languages via finite state automata, and dynamically construct Standard Young Tableaux. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11449 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weyl Groups and the Modified Kostant Game Castro, Alexander Caviedes Cortés-Cruz, Juan Sebastián Combinatorics 17B22, 20F55, 05E10, 14M15, 68Q45 This paper presents a generalization of the Kostant game, a combinatorial framework originally for generating positive roots in Lie algebras. By introducing an arbitrary multi-vertex modification, we prove that the resulting game configurations naturally biject with the minimal length representatives of parabolic quotients W/W_J. This yields a dynamical and algorithmic perspective on reduced words. Finally, we apply this framework to derive a novel root counting identity, formalize the Coxeter-theoretic foundation for combinatorial approaches to the Mukai conjecture, establish the regularity of reduced word languages via finite state automata, and dynamically construct Standard Young Tableaux. |
| title | Weyl Groups and the Modified Kostant Game |
| topic | Combinatorics 17B22, 20F55, 05E10, 14M15, 68Q45 |
| url | https://arxiv.org/abs/2605.11449 |