Subword Complexes and Nil-Hecke Moves
For a finite Coxeter group W, a subword complex is a simplicial complex associated with a pair (Q, ρ), where Q is a word in the alphabet of simple reflections, ρ is a group element. We describe the transformations of such a complex induced by nil-moves and inverse operations on Q in the nil-Hecke mo...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2013-01-01
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| Series: | Моделирование и анализ информационных систем |
| Subjects: | |
| Online Access: | http://mais-journal.ru/jour/article/view/163 |
| _version_ | 1797967980479381504 |
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| author | M. A. Gorsky |
| author_facet | M. A. Gorsky |
| author_sort | M. A. Gorsky |
| collection | DOAJ |
| description | For a finite Coxeter group W, a subword complex is a simplicial complex associated with a pair (Q, ρ), where Q is a word in the alphabet of simple reflections, ρ is a group element. We describe the transformations of such a complex induced by nil-moves and inverse operations on Q in the nil-Hecke monoid corresponding to W. If the complex is polytopal, we also describe such transformations for the dual polytope. For W simply-laced, these descriptions and results of [5] provide an algorithm for the construction of the subword complex corresponding to (Q, ρ) from the one corresponding to (δ(Q), ρ), for any sequence of elementary moves reducing the word Q to its Demazure product δ(Q). The former complex is spherical or empty if and only if the latter one is empty. The article is published in the author’s wording. |
| first_indexed | 2024-04-11T02:39:50Z |
| format | Article |
| id | doaj.art-42fe1d07bca2427f83a2a7dce0faad4a |
| institution | Directory Open Access Journal |
| issn | 1818-1015 2313-5417 |
| language | English |
| last_indexed | 2024-04-11T02:39:50Z |
| publishDate | 2013-01-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj.art-42fe1d07bca2427f83a2a7dce0faad4a2023-01-02T19:14:01ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172013-01-01206121128157Subword Complexes and Nil-Hecke MovesM. A. Gorsky0Математический Институт им. В. А. Стеклова РАН; Университет Париж Дидро; Математический Институт ЖюссьёFor a finite Coxeter group W, a subword complex is a simplicial complex associated with a pair (Q, ρ), where Q is a word in the alphabet of simple reflections, ρ is a group element. We describe the transformations of such a complex induced by nil-moves and inverse operations on Q in the nil-Hecke monoid corresponding to W. If the complex is polytopal, we also describe such transformations for the dual polytope. For W simply-laced, these descriptions and results of [5] provide an algorithm for the construction of the subword complex corresponding to (Q, ρ) from the one corresponding to (δ(Q), ρ), for any sequence of elementary moves reducing the word Q to its Demazure product δ(Q). The former complex is spherical or empty if and only if the latter one is empty. The article is published in the author’s wording.http://mais-journal.ru/jour/article/view/163комплексы подсловгруппы Кокстераниль-моноиды Гекке |
| spellingShingle | M. A. Gorsky Subword Complexes and Nil-Hecke Moves Моделирование и анализ информационных систем комплексы подслов группы Кокстера ниль-моноиды Гекке |
| title | Subword Complexes and Nil-Hecke Moves |
| title_full | Subword Complexes and Nil-Hecke Moves |
| title_fullStr | Subword Complexes and Nil-Hecke Moves |
| title_full_unstemmed | Subword Complexes and Nil-Hecke Moves |
| title_short | Subword Complexes and Nil-Hecke Moves |
| title_sort | subword complexes and nil hecke moves |
| topic | комплексы подслов группы Кокстера ниль-моноиды Гекке |
| url | http://mais-journal.ru/jour/article/view/163 |
| work_keys_str_mv | AT magorsky subwordcomplexesandnilheckemoves |