تقرير
On an $n$-ary generalization of the Lie representation
| العنوان: | On an $n$-ary generalization of the Lie representation |
|---|---|
| المؤلفون: | Friedmann, Tamar, Hanlon, Phil, Wachs, Michelle L. |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, Mathematics - Representation Theory |
| الوصف: | We continue our study, initiated in our prior work with Richard Stanley, of the representation of the symmetric group on the multilinear component of an $n$-ary generalization of the free Lie algebra known as the free Fillipov $n$-algebra with $k$ brackets. Our ultimate aim is to determine the multiplicities of the irreducible representations in this representation. This had been done for the ordinary Lie representation ($n=2$ case) by Kraskiewicz and Weyman. The $k=2$ case was handled in our prior work, where the representation was shown to be isomorphic to $S^{2^{n-1}1}$. In this paper, for general $n$ and $k$, we obtain decomposition results that enable us to prove that in the $k=3$ case, the representation is isomorphic to $S^{3^{n-1}1} \oplus S^{3^{n-2}21^2}$. Comment: 18 pages; Notation as in arXiv:1710.00376 [math.CO] and arXiv:2307.00587 [math.CO]; v2: 20 pages, minor changes and improved version of Corollary 3.4 moved to Section 4 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2402.19174 |
| رقم الأكسشن: | edsarx.2402.19174 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |