Computability in Europe 2006
Logical Approaches to Computational Barriers

Special Session Talk:
A quantum information-theoretic proof of the relation between Horn's problem and the Littlewood-Richardson coefficients

Speaker: Matthias Christandl
Author(s): Matthias Christandl


Horn's problem asks for the conditions on sets of integers mu,
nu and lambda that ensure the existence of Hermitian operators
A, B and A+B with spectra mu, nu and lambda,
respectively. It has been shown that this problem is equivalent to
deciding whether the irreducible representation of GL(d) with highest weight
lambda is contained in the tensor product of irreducible representations with
highest weight mu and nu. In this paper we present a
quantum information-theoretic proof of the relation between the two
problems that is asymptotic in one direction. This result has
previously been obtained by Klyachko using geometric invariant
theory. The work presented in this paper does not,
however, touch upon the non-asymptotic equivalence between the two problems, a
result that rests on the recently proven saturation conjecture for GL(d).

websites: Arnold Beckmann 2008-03-20