Characters of central piques

As a first step towards a duality theory for central quasigroups, the paper presents an explicit computation of the characters of a central pique (quasigroup with pointed idempotent) using Wignerʹs “little groups” method. The characters of a central piqueʹs cloop (principally isotopic abelian group) form a dual pique. The conjugacy classes of the dual correspond to the characters of the primal; indeed the unitary character table of the dual is the inverse of the unitary character table of the primal. Together with its dual, a central pique forms a structure known as the double. The double satisfies identities indexed by loops of 2-power order. These identities project onto the unit circle to yield identities involving character values.