关于$\SL_3(k)$和PDMATHAAB- $\GL_3(k)$的Jensen模和倾斜模的一个结果的注记
Some remarks on a result of Jensen and tilting modules for $\SL_3(k)$ and $q$-$\GL_3(k)$
摘要：
本文回顾了Jensen关于$\SL_3(k)$的某些倾斜模的特征的一个结果，其中$k$的特征至少为5，填补了该结果证明中的一些空白.然后，我们将结果应用到寻找一些分解数的三部分划分的对称群和Hecke代数。我们回顾一下已知的特征二和特征三。量子的情况下，也被认为是：类似的结果举行的混合量子群，其中$q$是一个$l$ th根的单位与$l$至少有三个，因此也适用于相关的Hecke代数。
英文摘要：
This paper reviews a result of Jensen on characters of some tilting modules for $\SL_3(k)$, where $k$ has characteristic at least five and fills in some gaps in the proof of this result. We then apply the result to finding some decomposition numbers for three part partitions for the symmetric group and the Hecke algebra. We review what is known for characteristic two and three. The quantum case is also considered: analogous results hold for the mixed quantum group where $q$ is an $l$th root of unity with $l$ at least three and thus also hold for the associated Hecke algebra.
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