Extended Weak Order for the Rank 3 Universal Coxeter Group
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912562925273088 |
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| author | Barkley, Grant Defant, Colin Hersh, Patricia McCammond, Jon McConville, Thomas Speyer, David E |
| author_facet | Barkley, Grant Defant, Colin Hersh, Patricia McCammond, Jon McConville, Thomas Speyer, David E |
| contents | The weak order is a classical poset structure on a Coxeter group; it is a lattice when the group is finite but merely a meet-semilattice when the group is infinite. Motivated by problems in Kazhdan--Lusztig theory, Matthew Dyer introduced the extended weak order, a poset that contains a copy of the weak order as an order ideal, and he conjectured that the extended weak order for any Coxeter group is a lattice. We prove Dyer's conjecture for the rank 3 universal Coxeter group. This is the first non-spherical, non-affine Coxeter group for which Dyer's conjecture has been proven. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_00871 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extended Weak Order for the Rank 3 Universal Coxeter Group Barkley, Grant Defant, Colin Hersh, Patricia McCammond, Jon McConville, Thomas Speyer, David E Combinatorics Group Theory 20F55, 17B22, 06B23 The weak order is a classical poset structure on a Coxeter group; it is a lattice when the group is finite but merely a meet-semilattice when the group is infinite. Motivated by problems in Kazhdan--Lusztig theory, Matthew Dyer introduced the extended weak order, a poset that contains a copy of the weak order as an order ideal, and he conjectured that the extended weak order for any Coxeter group is a lattice. We prove Dyer's conjecture for the rank 3 universal Coxeter group. This is the first non-spherical, non-affine Coxeter group for which Dyer's conjecture has been proven. |
| title | Extended Weak Order for the Rank 3 Universal Coxeter Group |
| topic | Combinatorics Group Theory 20F55, 17B22, 06B23 |
| url | https://arxiv.org/abs/2509.00871 |