Finite dimensional varieties on hypergroups

Abstract Let X be a hypergroup, K its compact subhypergroup and assume that (X, K) is a Gelfand pair. Connections between finite dimensional varieties and K-polynomials on X are discussed. It is shown that a K-variety on X is finite dimensional if and only if it is spanned by finitely many K-monomials. Next, finite dimensional varieties on affine groups over $${\mathbb {R}}^d$$ R d , where d is a positive integer are discussed. A complete description of those varieties using partial differential equations is given.