论文标题
$ \ frac {n！} {2} $ supendure for Hook形状的证明
A proof of the $\frac{n!}{2}$ conjecture for hook shapes
论文作者
论文摘要
转换后的MacDonald多项式$ \ widetilde {h}_μ（z; t，q）$的众所周知的表示模型，其中$μ$是整数分区，由Garsia-Haiman模块$ \ Mathcal $ \ Mathcal {H}_μ$ $。我们研究了Bergeron和Garsia的$ \ frac {n！} {k} $猜想，这涉及在交叉点下的某些$ k $ tuplase garsia-haiman模块的行为。在特殊情况下，$μ$具有挂钩形状，我们使用$ \ Mathcal {h}_μ$的基础，这是由于Adin，Remmel和Roichman引起的，可以通过构建两个Garsia-Haiman模块的相互作用来解决$ \ frac {n！} {N！} {2} $ conjocture。
A well-known representation-theoretic model for the transformed Macdonald polynomial $\widetilde{H}_μ(Z;t,q)$, where $μ$ is an integer partition, is given by the Garsia-Haiman module $\mathcal{H}_μ$. We study the $\frac{n!}{k}$ conjecture of Bergeron and Garsia, which concerns the behavior of certain $k$-tuples of Garsia-Haiman modules under intersection. In the special case that $μ$ has hook shape, we use a basis for $\mathcal{H}_μ$ due to Adin, Remmel, and Roichman to resolve the $\frac{n!}{2}$ conjecture by constructing an explicit basis for the intersection of two Garsia-Haiman modules.
