Wolosz János: Symmetric and exterior squares of hook representations

Abstract:
Denote by M^{\lambda} the irreducible CS_n-representation of the symmetric group corresponding to the Young diagram \lambda.
With this notation V=M^{(n-1,1)} is the standard representation of degree n-1.
The hook representations are irreducible CS_n-representations, which are the k-th exterior power of V. These representations are corresponding to Young diagrams (n-k, 1^{k}).
J. B. Remmel determined the multiplicities of irreducible summands of the tensor squares of hook representations for all n, k.

In the present talk, we will give a brief introduction to hook representations, and show a method how to get the irreducible decomposition of the
symmetric and exterior squares of these representations.