A subgroup of special linear group

Question

Does anybody know if the subgroup of diagonal and antidiagonal matrices of $SL(n,F)$ has been given a particular name?

By $SL(n,F)$

I mean $n \times n$ matrices over a field $F$ with determinant 1. An $n \times n$ matrix $A=(a_{ij})$ is antidiagonal if $a_{ij} \neq 0$ only if $i+j = n$.