CHARACTERS OF PARAMODULAR GROUPS AND SOME EXTENSIONS

Abstract

ABSTRACT For P a rational symmetric positive-definite matrix of dimension let be the paramodular group of degree g and level P. We determine , the group of abelian characters of . In all cases is a subgroup of . The characters can be realized via homomorphisms for some finite groups G, such as for , and certain new finite analogs of paramodular groups. The characters are explicitly known (on generators at least). All characters arise as multiplier-systems of certain paramodular forms also. Moreover in the case of degree 2 we use the characters of , to determine all the characters of the well-known maximal normal discrete extension.