Reference request: representation theory of the hyperoctahedral group 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 $C_2$). 
 A: I liked the references of Kerber listed in the wikipedia article.  The most relevant chapter is available online, along with both volumes which were quite useful.
Kerber's presentation focusses on the idea that H is going to be cyclic and specifically handles H of order 2, but like MacDonald handles general H abstractly.  GAP handles the hyper-octahedral group this way too, using generic code for wreath products written more or less solely for the hyper-octahedral group.  The "bi" in bi-partitions just refers to the two conjugacy classes of C2, and the general theory replaces "bi" by however many conjugacy classes H has.
A: As Bruce Westbury suggested at another question, the following book might be mentioned here.
A. V. Zelevinsky, Representations of Finite Classical Groups A Hopf algebra approach; Lecture Notes in Mathematics 869 (1981)
It is unfortunately probably hard to get anymore, and its typography is not very attractive, but I find the treatment very elegant. The representation theory of $S_n$ gives rise to an algebraic structure called Positive Self-Adjoint Hopf-algebra, whose simplest nontrivial model is the ring of symmetric functions with a comultiplication. Its combinatorial structure is entirely deduced from the axioms, and it provides models for among other things the representations rings for finite linear groups and for wreath products of the symmetric groups. Thus the hyperoctahedral groups are treated nicely as a simple special case.
A: This is quite late but I've been playing around with type BC Coxeter group representations recently and thought I'd provide a nice reference I've found for anyone else that is interested: Alun Morris provides a construction of all the irreducible representations of the hyperoctahedral group (in characteristic zero) via an extension of the usual 'polytabloid' combinatorial machinery from type A in
"Representations of Weyl Groups over and arbitrary field", A.O. Morris; 'Young Tableaux and Schur Functors in algebra and geometry' Asterisque 87-88 (1981) p.267-288
A 'straightening algorithm' is provided by H. Can, here.
It should be noted that these articles provide a more computational approach to the representations introduced in I.G. Macdonald's paper referenced by Jim Humphreys in the comment to Vinoth's question.
A: There is a paper: Representations of the hyperoctahedral groups by L. Geissinger and D. Kinch.
A: The theory extends to the wreath product of a cyclic group $C$ with the symmetric group $S_n$.
Then we are looking at a list of $|C|$ partitions with a total of $n$ boxes. This is in MacDonald so I expect you know this.
Now we can deform these group algebras analogously to deforming the group algebras of $S_n$ to Hecke algebras. The group algebra of the cyclic groups is deformed to $K[x]/p(x)$
where the degree of $p$ is $|C|$ where originally we had $x^{|C|}=1$. These are known as Ariki-Koike algebras and there is an extensive literature on these.
Even if you are only interested in hyperoctahedral groups you may find papers on Ariki-Koike algebras which give you what you want by specialising. For example, I have seen the semi-normal form for Ariki-Koike algebras but not for hyperoctahedral groups.
A: A paper dealing with the hyperoctahedral group :
"Branching rules for the hyperoctahedral group",J.Math.Phys.30,11,1989,pp2469-2475.
