Chi-map isomorphism conjecture for wreath product algebras

For each $m\in\mathbb{N}$, let $\chi_m$ denote the algebra map defined in the paper. Chi-map isomorphism conjecture. The map $\chi_m$ is an isomorphism of algebras for all $m\in\mathbb{N}$. This is a generalization of the corresponding result known when $B=\mathbb{F}$; the source also identifies it with a conjecture of Cautis and Licata in their special case.