论文标题
在与Hecke代数的表示相关的正交预测上
On orthogonal projections related to representations of the Hecke algebra on a tensor space
论文作者
论文摘要
我们考虑找到等级$ r $的正交预测的问题，这引起了Hecke代数$ h_n（q）$的代表，其中代数ACT的发电机在$ n $ th $ th th the $ n $ th-th the-th $ th-th the-th $ th-th the-th $ th-th the-th。结果表明，这样的预测是一定功能的全球最小值。还表明，此类预测的特征属性是，如果$ p $产生代表temperley-lieb代数，则某些积极的确定矩阵$ a $只有两个特征值或一个特征值。除了参数$ n $，$ r $和$ q = q + q^{ - 1} $之外，另一个参数$ k $被证明是投影$ p $的有用特征。特别是，当$ n $和$ r $的值固定时，我们使用它为$ q $提供了一个下限，并且我们证明$ k = r n $时，并且仅当$ p $属于temperley-lieb类型。此外，我们提出了一种构建预测$ p $的方法，并以$ n = 3 $进行一些新颖的例子。
We consider the problem of finding orthogonal projections $P$ of a rank $r$ that give rise to representations of the Hecke algebra $H_N(q)$ in which the generators of the algebra act locally on the $N$-th tensor power of the space ${\mathbb C}^n$. It is shown that such projections are global minima of a certain functional. It is also shown that a characteristic property of such projections is that a certain positive definite matrix $A$ has only two eigenvalues or only one eigenvalue if $P$ gives rise to a representation of the Temperley-Lieb algebra. Apart from the parameters $n$, $r$, and $Q=q + q^{-1}$, an additional parameter $k$ proves to be a useful characteristic of a projection $P$. In particular, we use it to provide a lower bound for $Q$ when the values of $n$ and $r$ are fixed and we show that $k=r n$ if and only if $P$ is of the Temperley-Lieb type. Besides, we propose an approach to constructing projections $P$ and give some novel examples for $n=3$.
