[{"data":1,"prerenderedAt":4},["ShallowReactive",2],{"jYGbJx7dHy":3},"# Coxeter Groups in Lean\n\nWe formalize in Lean some results on Coxeter groups, following the textbooks [[1]](#ref1) and [[2]](#ref2). The results are organized as follows:\n\n* [Basic.lean](Coxeter/Basic.lean)\n    * Basic definitions and lemmas\n    * The opposite of a Coxeter group\n* [PermutationRepresentation.lean](Coxeter/PermutationRepresentation.lean)\n    * Construction of the permutation representation\n* [StrongExchange.lean](Coxeter/StrongExchange.lean)\n    * Strong exchange\n    * Deletion property\n* [Bruhat.lean](Coxeter/Bruhat.lean)\n    * Definition of the Bruhat order\n    * Subword property\n    * Lifting property\n    * The longest element of a finite Coxeter group\n* [GeometricRepresentation.lean](Coxeter/GeometricRepresentation.lean)\n    * Construction of the geometric representation\n    * Order of $s_i s_{i'}$\n    * Injectivity of `cs.simple`\n\n## References\n\n\u003Ca name=\"ref1\">[1]\u003C/a>: A. Björner and F. Brenti, *Combinatorics of Coxeter Groups*. Springer, 2005. DOI: [10.1007/3-540-27596-7](https://doi.org/10.1007/3-540-27596-7)\n\n\u003Ca name=\"ref2\">[2]\u003C/a>: N. Bourbaki, *Groupes et algèbres de Lie*. Springer, 2007. DOI: [10.1007/978-3-540-34491-9](https://doi.org/10.1007/978-3-540-34491-9)\n",1791742520057]