Action of special linear groups to the tensor of indeterminates, classical invariants of binary forms and hyperdeterminant

Mitsuhiro Miyazaki

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arXiv · 1301.6979

Action of special linear groups to the tensor of indeterminates, classical invariants of binary forms and hyperdeterminant

Mitsuhiro Miyazaki

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Abstract

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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Mitsuhiro Miyazaki. 2013-01-29. Action of special linear groups to the tensor of indeterminates, classical invariants of binary forms and hyperdeterminant. https://arxiv.org/abs/1301.6979

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