We relate the character theory of symmetric groups S2n and S2n+1 with that hyperoctahedral group Bn=(Z/2)n⋊Sn, as part expectation reductive diagram automorphism their Weyl groups, is related to fixed subgroup automorphism.

The conditions under which, multilinear forms (the symmetric case and the non symmetric case),can be written as a product of linear forms, are considered. Also we generalize a result due to S.Kurepa for 2n-functionals in a group G.