Coxeter groups and Billey-Postnikov decompositions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914937937330176 |
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| author | Oh, Suho Richmond, Edward |
| author_facet | Oh, Suho Richmond, Edward |
| contents | In this chapter, we give an overview of Billey-Postnikov (BP) decompositions which have become an important tool for understanding the geometry and combinatorics of Schubert varieties. BP decompositions are factorizations of Coxeter group elements with many nice properties in relation to Bruhat partial order. They have played an important role in the classification and enumeration of smooth Schubert varieties. They have also been used in the study of inversion hyperplane arrangements and permutation pattern avoidance. We survey many of these applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03096 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coxeter groups and Billey-Postnikov decompositions Oh, Suho Richmond, Edward Combinatorics 20F55, 14M15, 52C35 In this chapter, we give an overview of Billey-Postnikov (BP) decompositions which have become an important tool for understanding the geometry and combinatorics of Schubert varieties. BP decompositions are factorizations of Coxeter group elements with many nice properties in relation to Bruhat partial order. They have played an important role in the classification and enumeration of smooth Schubert varieties. They have also been used in the study of inversion hyperplane arrangements and permutation pattern avoidance. We survey many of these applications. |
| title | Coxeter groups and Billey-Postnikov decompositions |
| topic | Combinatorics 20F55, 14M15, 52C35 |
| url | https://arxiv.org/abs/2409.03096 |