-д хадгалсан:
| Үндсэн зохиолч: | |
|---|---|
| Формат: | Preprint |
| Хэвлэсэн: |
2020
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| Нөхцлүүд: | |
| Онлайн хандалт: | https://arxiv.org/abs/2003.10700 |
| Шошгууд: |
Шошго нэмэх
Шошго байхгүй, Энэхүү баримтыг шошголох эхний хүн болох!
|
Агуулга:
- The Frobenius characteristic of $Lie_n,$ the representation of the symmetric group $S_n$ afforded by the multilinear component of the free Lie algebra, is known to satisfy many interesting plethystic identities. In this paper we prove a conjecture of Richard Stanley establishing the plethystic inverse of the sum $\sum_{n\geq 0} Lie_{2n+1}$ of the odd Lie characteristics. We obtain an apparently new plethystic decomposition of the regular representation of $S_n$ in terms of irreducibles indexed by hooks, and the Lie representations. We determine the plethystic inverse of the alternating sum of the odd Lie characteristics.