Euler–Mahonian distributions of type BnBn

Adin, Brenti, and Roichman introduced the pairs of statistics (ndes,nmaj) and (fdes,fmaj). They showed that these pairs are equidistributed over the hyperoctahedral group BnBn, and can be considered “Euler–Mahonian” in the sense that they generalize the Carlitz identity. Further, they asked whether there exists a bijective proof of the equidistribution of their statistics. We give such a bijection, along with a new proof of the generalized Carlitz identity.