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I'm trying to understand the paper "Products and plethysms of characters with orthogonal, symplectic, and symmetric groups" by D.E. Littlewood (link), but I'm having trouble overcoming the language that he uses (it's from 1958, which might be the problem?).

In particular, one word he uses a lot is "concomitant". A google search for the definition turned out to be extremely unhelpful, but I think this is something really basic that a lot of people here know.

As a bonus, I'm really just trying to understand the passage on p.25 between Theorem VII and Theorem VIII. As I understand it, the "fundamental forms" he mentions are the functions $S_i$ defined on p.24, but when applying these to $\bigwedge^2 {\bf C}^n$, I'm getting 0, but $\bigwedge^2 {\bf C}^n$ this is not an irreducible representation of the symmetric group $\mathfrak{S}_n$ (he seems to be claiming that the intersection of the kernels of the fundamental forms should be). The reference he mentions doesn't seem to be of much help either.

So concrete questions:

1. What does he mean by concomitant?
2. Does anyone understand the passage on p.25 (and can you please explain to me)?
2 fixed "contomitant"

I'm trying to understand the paper "Products and plethysms of characters with orthogonal, symplectic, and symmetric groups" by D.E. Littlewood (link), but I'm having trouble overcoming the language that he uses (it's from 1958, which might be the problem?).

In particular, one word he uses a lot is "concomitant". A google search for the definition turned out to be extremely unhelpful, but I think this is something really basic that a lot of people here know.

As a bonus, I'm really just trying to understand the passage on p.25 between Theorem VII and Theorem VIII. As I understand it, the "fundamental forms" he mentions are the functions $S_i$ defined on p.24, but when applying these to $\bigwedge^2 {\bf C}^n$, I'm getting 0, but $\bigwedge^2 {\bf C}^n$ this is not an irreducible representation of the symmetric group $\mathfrak{S}_n$ (he seems to be claiming that the intersection of the kernels of the fundamental forms should be). The reference he mentions doesn't seem to be of much help either.

So concrete questions:

1. What does he mean by contomitantconcomitant?
2. Does anyone understand the passage on p.25 (and can you please explain to me)?
1

# What is a concomitant (and other questions on D.E. Littlewood's "Products and plethysms of characters with orthogonal, symplectic, and symmetric groups" )?

I'm trying to understand the paper "Products and plethysms of characters with orthogonal, symplectic, and symmetric groups" by D.E. Littlewood (link), but I'm having trouble overcoming the language that he uses (it's from 1958, which might be the problem?).

In particular, one word he uses a lot is "concomitant". A google search for the definition turned out to be extremely unhelpful, but I think this is something really basic that a lot of people here know.

As a bonus, I'm really just trying to understand the passage on p.25 between Theorem VII and Theorem VIII. As I understand it, the "fundamental forms" he mentions are the functions $S_i$ defined on p.24, but when applying these to $\bigwedge^2 {\bf C}^n$, I'm getting 0, but $\bigwedge^2 {\bf C}^n$ this is not an irreducible representation of the symmetric group $\mathfrak{S}_n$ (he seems to be claiming that the intersection of the kernels of the fundamental forms should be). The reference he mentions doesn't seem to be of much help either.

So concrete questions:

1. What does he mean by contomitant?
2. Does anyone understand the passage on p.25 (and can you please explain to me)?