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arXiv · 1510.08420

Hilbert series and degree bounds for matrix (semi-)invariants

Visu Makam
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Abstract

We study the ring R(n,m) of invariants for the left-right action of SL_n \times SL_n on m-tuples of n by n complex matrices. We show that R(3,m) is generated by invariants of degree less equal 309 for all m. Then, we use a combinatorial description of the invariants to show that R(n,m) cannot be generated by invariants of degree < n^2 for large m. We also compute the Hilbert series for several cases.

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BibTeXRIS

Visu Makam. 2015-10-28. Hilbert series and degree bounds for matrix (semi-)invariants. https://arxiv.org/abs/1510.08420

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