Super-cocharacters,star-cocharacters and multiplicities bounded by one

Let A be an algebra over a field of characteristic zero with an additional structure of superalgebra or algebra with involution. The ordinary representation theory of the hyperoctahedral group is exploited in order to study the super-identities or the star-identities of A. One associates to A a sequence -characters and one of the main objective of the theory is to determine their decomposition into irreducibles. Here we classify the super-identities and the star-identities in case the corresponding multiplicities are bounded by one. This is strictly related to the varieties of algebras whose lattice of subvarieties is distributive. A. Giambruno was partially supported by MIUR of Italy. S. Mishchenko was partially supported by RFBR grant 07-01-00080.