The coinvariant algebra of the symmetric group as a direct sum of induced modules
Morita, Hideaki ; Nakajima, Tatsuhiro
Osaka J. Math., Tome 42 (2005) no. 1, p. 217-231 / Harvested from Project Euclid
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Let $R_n$ be the coinvariant algebra of the symmetric group $S_n$. The algebra has a natural gradation. For a fixed $l$ ($1\leq l \leq n$), let $R_n(k;l)$ ($0\leq k\leq l-1$) be the direct sum of all the homogeneous components of $R_n$ whose degrees are congruent to $k$ modulo $l$. In this article, we will show that for each $l$ there exists a subgroup $H_{l}$ of $S_n$ and a representation $\Psi(k;l)$ of $H_{l}$ such that each $R_n(k;l)$ is induced by $\Psi(k;l)$.
Publié le : 2005-03-14
Classification:  
@article{1153494323,
     author = {Morita, Hideaki and Nakajima, Tatsuhiro},
     title = {The coinvariant algebra of the symmetric group as a direct sum of induced modules},
     journal = {Osaka J. Math.},
     volume = {42},
     number = {1},
     year = {2005},
     pages = { 217-231},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1153494323}
}

Morita, Hideaki; Nakajima, Tatsuhiro. The coinvariant algebra of the symmetric group as a direct sum of induced modules. Osaka J. Math., Tome 42 (2005) no. 1, pp.  217-231. http://gdmltest.u-ga.fr/item/1153494323/