特殊线性群对不定式张量、二元形式经典不变量和超行列式的作用
Action of special linear groups to the tensor of indeterminates, classical invariants of binary forms and hyperdeterminant
摘要：
本文研究了SL（m，K）\times SL（n，K）和SL（m，K）\times SL（n，K）\times SL（2，K）作用于m \times n \times 2的三维不定式阵列上的不变量环，其中K是无限域.证明了若m= \geq 2，则SL（n，K）\times SL（n，K）-不变量的环是由K上n+1个代数无关元生成的，SL（2，K）在该环上的作用与经典的二元形式不变量理论中定义的作用相同.当m为\neq n时，我们还完全揭示了SL（m，K）\times SL（n，K）-不变量和SL（m，K）\times SL（n，K）\times SL（2，K）-不变量的环.
英文摘要：
In this paper, we study the ring of invariants under the action of SL(m,K)\times SL(n,K) and SL(m,K)\times SL(n,K)\times SL(2,K) on the 3-dimensional array of indeterminates of form m\times n\times 2, where K is an infinite field. And we show that if m=n\geq 2, then the ring of SL(n,K)\times SL(n,K)-invariants is generated by n+1 algebraically independent elements over K and the action of SL(2,K) on that ring is identical with the one defined in the classical invariant theory of binary forms. We also reveal the ring of SL(m,K)\times SL(n,K)-invariants and SL(m,K)\times SL(n,K)\times SL(2,K)-invariants completely in the case where m\neq n.
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