体积和快速矩阵乘法
Plethysm and fast matrix multiplication
摘要：
受对称矩阵乘法的启发，我们研究了李群$SL_n$的伴随表示$\mathfrak{sl}_n$的体积模$S^k(\mathfrak{sl}_n)$.特别是，我们描述了分解成不可约组件的$k=3$，并找到所有不可约组件的最高权向量。关系到快速矩阵乘法，特别是Coppersmith-Winograd张量。
英文摘要：
Motivated by the symmetric version of matrix multiplication we study the plethysm $S^k(\mathfrak{sl}_n)$ of the adjoint representation $\mathfrak{sl}_n$ of the Lie group $SL_n$. In particular, we describe the decomposition of this representation into irreducible components for $k=3$, and find highest weight vectors for all irreducible components. Relations to fast matrix multiplication, in particular the Coppersmith-Winograd tensor are presented.
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