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Let R(S) (resp. R(G)) be the sum of the Grothendieck groups of the categories of the smooth representations of finite length of the groups Sp(n, F )’s (resp. GSp(n, F )’s). Using the functor of the parabolic induction one can define a structure of R-modules on R(S) and R(G) (see the first section). These multiplications are denoted by  . They induce biadditive mappings µ : R ⊗ R(S) → R(S)

Induced representations and classification for $GSp(2,F)$ and $Sp(2,F)$