We construct a family of $S_n$ modules indexed by $c\in \{1,\dots ,n\}$ with the property that upon restriction to $S_{n-1}$ they recover the classical parking function representation of Haiman. The construction of these modules relies on an $S_n$-action on a set that is closely related to the set of parking functions. We compute the characters of these modules and use the resulting description to classify them up to isomorphism. In particular, we show that the number of isomorphism classes is equal to the number of divisors d of n satisfying $d\ne 2(\mathrm{mod}4)$. In the cases $c=n$ and $c=1$, we compute the number of orbits. Based on empirical evidence, we conjecture that when $c=1$, our representation is h-positive and is in fact the (ungraded) extension of the parking function representation constructed by Berget and Rhoades.

我们建立了一个家庭 ${\mathrm{小号}}_{ñ}$ 索引的模块 $C\in \{\mathrm{1个}，\dots ，ñ\}$ 具有限制于 ${\mathrm{小号}}_{ñ-\mathrm{1个}}$他们恢复了Haiman的经典停车功能表示。这些模块的构建依赖于${\mathrm{小号}}_{ñ}$-与一组停车功能密切相关的一组动作。我们计算这些模块的特征，并使用结果描述将它们分类为同构。特别是，我们表明，同构类的个数等于除数的数量ð的ñ满足$d\ne 2（\mathrm{模}4）$。在这种情况下$C=ñ$ 和 $C=\mathrm{1个}$，我们计算轨道数。根据经验证据，我们推测$C=\mathrm{1个}$，我们的表示是h阳性的，实际上是Berget和Rhoades构造的停车功能表示的（未分级）扩展。