Hilbert series and degree bounds for matrix (semi-)invariants
Representation Theory
2015-10-29 v1 Commutative Algebra
Combinatorics
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.
Keywords
Cite
@article{arxiv.1510.08420,
title = {Hilbert series and degree bounds for matrix (semi-)invariants},
author = {Visu Makam},
journal= {arXiv preprint arXiv:1510.08420},
year = {2015}
}
Comments
13 pages, 1 figure