On transfer of automorphic structures related with orthogonal and symplectic groups

An automorphic structure related with (arithmetical) discrete subgroup of a Lie group is a diagonalizable linear representation of Hecke–Shimura algebra of this discrete subgroup on a space of automorphic forms by Hecke operators together with Euler products (zeta functions) associated to common eigenfunctions of the operators. By transfer of automorphic structures related with two groups we understand an embedding of corresponding spaces of automorphic forms compatible with the action of Hecke operators and relatting the relevant zeta functions. Traditionally they were considering "lifts" of automorphic structures to similar groups of higher order such as lifts of automorphic structures on $SL_n$ or Saito–Kurokawa and Ikeda lifts for Siegel modular forms. Recently were considered examples of transfer of automorphic structures related with quite different groups. In this talk we will discuss the transfer of automorphic structures related with (finite) groups of integral units of integral positive definite quaternary quadratic forms and subgroups of the Siegel modular group of genus 2. No special knowledge is presupposed.