Arithmetic quantum unique ergodicity for products of hyperbolic 2

Lior Silberman, Zvi Shem-Tov

Abstract: We prove the arithemtic quantum unique ergodicity (AQUE) conjecture for sequences of Hecke--Maass forms on quotients Γ∖(H(2))r×(H(3))s. An argument by induction on dimension of the orbit allows us to rule out the limit measure concentrating on closed orbits of proper subgroups despite many returns of the Hecke correspondence to neighborhoods of the orbit.