I was wondering if someone knows a good reference for the representation theory of the hyper-octahedral group $G$. The hyper-octahedral group $G$ is defined as the wreath product of $C_2$ (cyclic group order $2$) with $S_n$ (symmetric group on $n$ letters).

I understand that the representations of $G$ are in bijection with bi-partitions of $n$. I am looking for a reference which explains the details of why the representations of $G$ are in bijection with bi-partitions of $n$, and constructs the irreducible representations of $G$ (I imagine this is vaguely similar to the construction of Specht modules for $S_n$).

So far, the only reference I have is an Appendix of MacDonald's "Symmetric functions and Hall polynomials" (2nd version), which deals with the representation theory of the wreath product of $H$ with $S_n$ (for $H$ being an arbitrary group, not $C_2$).

Some irreducible representations of Weyl groups(Bull. LMS, 1972) with reference to W. Specht's 1937 paperDarstellungstheorie der Hyperoktaedergruppe. But more recent references are suggested in the answers here. $\endgroup$ – Jim Humphreys May 23 '10 at 13:20Finite Groups of Lie Type, section 11.4, along with his references to Macdonald and Lusztig. $\endgroup$ – Jim Humphreys Jan 2 '17 at 18:16