Syzygies for the vector invariants of the dihedral group

Domokos, Mátyás (2024) Syzygies for the vector invariants of the dihedral group. JOURNAL OF ALGEBRA, 641. pp. 9-26. ISSN 0021-8693

Preview

Text 2207.04495v2.pdf Download (273kB) | Preview

Abstract

The dihedral group D2n of order 2n acts on the space of m-tuples of vectors from its defining 2-dimensional representation. The corresponding algebra of polynomial invariants has a natural structure as a module over the general linear group GLm(C). Therefore the ideal of relations between the generators of the algebra of invariants can be treated as a GL-ideal (i.e. an ideal stable with respect to the appropriate action of GLm(C)). It is shown that this GL-ideal is generated by relations depending on no more than 3 vector variables. A minimal GL-ideal generating system is found for the cases of m = 2 and an arbitrary n, and for the cases of an arbitrary m and n = 4, n = 5, and n = 6. (c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by -nc -nd /4 .0/).

Actions (login required)

Edit Item