تقرير
Regular Schur labeled skew shape posets and their 0-Hecke modules
| العنوان: | Regular Schur labeled skew shape posets and their 0-Hecke modules |
|---|---|
| المؤلفون: | Kim, Young-Hun, Lee, So-Yeon, Oh, Young-Tak |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Representation Theory, Mathematics - Combinatorics, 20C08, 06A07, 05E10, 05E05 |
| الوصف: | Assuming Stanley's $P$-partition conjecture holds, the regular Schur labeled skew shape posets with underlying set $\{1,2,\ldots, n\}$ are precisely the posets $P$ such that the $P$-partition generating function is symmetric and the set of linear extensions of $P$, denoted $\Sigma_L(P)$, is a left weak Bruhat interval in the symmetric group $\mathfrak{S}_n$. We describe the permutations in $\Sigma_L(P)$ in terms of reading words of standard Young tableaux when $P$ is a regular Schur labeled skew shape poset, and classify $\Sigma_L(P)$'s up to descent-preserving isomorphism as $P$ ranges over regular Schur labeled skew shape posets. The results obtained are then applied to classify the $0$-Hecke modules $\mathsf{M}_P$ associated with regular Schur labeled skew shape posets $P$ up to isomorphism. Then we characterize regular Schur labeled skew shape posets as the posets whose linear extensions form a dual plactic-closed subset of $\mathfrak{S}_n$. Using this characterization, we construct distinguished filtrations of $\mathsf{M}_P$ with respect to the Schur basis when $P$ is a regular Schur labeled skew shape poset. Further issues concerned with the classification and decomposition of the $0$-Hecke modules $\mathsf{M}_P$ are also discussed. Comment: 44 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2310.20571 |
| رقم الأكسشن: | edsarx.2310.20571 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |