Classification of weak Bruhat interval modules of $0$-Hecke algebras
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916431973580800 |
|---|---|
| author | Yang, Han Yu, Houyi |
| author_facet | Yang, Han Yu, Houyi |
| contents | Weak Bruhat interval modules of the $0$-Hecke algebra in type $A$ provide a uniform approach to studying modules associated with noteworthy families of quasisymmetric functions. Recently this kind of modules were generalized from type $A$ to all Coxeter types. In this paper, we give an equivalent description, in a type-independent manner, when two left weak Bruhat intervals in a Coxeter group are descent-preserving isomorphic. As an application, we classify all left weak Bruhat interval modules of $0$-Hecke algebras up to isomorphism, and thereby answer an open question and resolve in the affirmative a conjecture of Jung, Kim, Lee, and Oh. Additionally, for finite Coxeter groups we show that the set of minimum (or maximum) elements of all left weak Bruhat intervals in each descent-preserving isomorphism class forms an interval under the right weak Bruhat order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07990 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classification of weak Bruhat interval modules of $0$-Hecke algebras Yang, Han Yu, Houyi Representation Theory Combinatorics Group Theory Rings and Algebras Weak Bruhat interval modules of the $0$-Hecke algebra in type $A$ provide a uniform approach to studying modules associated with noteworthy families of quasisymmetric functions. Recently this kind of modules were generalized from type $A$ to all Coxeter types. In this paper, we give an equivalent description, in a type-independent manner, when two left weak Bruhat intervals in a Coxeter group are descent-preserving isomorphic. As an application, we classify all left weak Bruhat interval modules of $0$-Hecke algebras up to isomorphism, and thereby answer an open question and resolve in the affirmative a conjecture of Jung, Kim, Lee, and Oh. Additionally, for finite Coxeter groups we show that the set of minimum (or maximum) elements of all left weak Bruhat intervals in each descent-preserving isomorphism class forms an interval under the right weak Bruhat order. |
| title | Classification of weak Bruhat interval modules of $0$-Hecke algebras |
| topic | Representation Theory Combinatorics Group Theory Rings and Algebras |
| url | https://arxiv.org/abs/2410.07990 |