Spectral rigidity of group actions: Applications to the case gr⟨𝑡,𝑠;𝑡𝑠=𝑠𝑡²⟩

Abstract

We apply a technique to study the notion of spectral rigidity of group actions to a group gr ⟨ t , s ;   t s = s t 2 ⟩ \mbox {gr}\langle t,s ; \ ts=st^2\rangle . As an application, we prove that there exist rank one weakly mixing transformations conjugate to its square, thereby giving a positive answer to a well-known question.