2022/07/10 by Domokos, M.
#20G05 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 13A50 #Representation Theory (math.RT) #Secondary 14L30
paper · doi:10.48550/arxiv.2207.04495
The problem of finding generators of the GL-ideal of the relations between the generators of the algebra of invariants of the dihedral group acting on m-tuples of vectors from its defining 2-dimensional representation is studied. 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 case when m=2, and for the case of the dihedral group of order 8 and arbitrary m.