论文标题
通过Brauer代数构建张量的无纹子投影
Construction of the traceless projection of tensors via the Brauer algebra
论文作者
论文摘要
我们描述了如何以封闭形式构建给定等级的无痕量投影。在实现这一目标的路上，我们调用了Brauer代数的表示理论和相关的Schur-Weyl二元性。由此产生的无可带投影仪是由纯粹的组合数据构建的，该数据涉及年轻图。通过施工，投影仪明显与对称组通勤，并适应了限制$ gl $ irredubirubirusirucirucirucirucirucirucirucirucirucirucirucirucirubirucirucirucirubirucirucirucirubirucimredcible。我们开发辅助计算技术，以利用应用程序的结果。构建无可观投影仪的拟议方法导致Brauer代数的半神经状态中的特定中心愿。
We describe how traceless projection of tensors of a given rank can be constructed in a closed form. On the way to this goal we invoke the representation theory of the Brauer algebra and the related Schur-Weyl dualities. The resulting traceless projector is constructed from purely combinatorial data involving Young diagrams. By construction, the projector manifestly commutes with the symmetric group and is well-adapted to restrictions to $GL$-irreducible tensor representations. We develop auxiliary computational techniques which serve to take advantage of the obtained results for applications. The proposed method of constructing traceless projectors leads to a particular central idempotent in the semisimple regime of the Brauer algebra.
