Why would multiplicities be log-concave ?

Details Why would multiplicities be log-concave ? Why would multiplicities be log-concave ?

2000-02-11

arxiv.org/abs/math/0002085v1

Mathematics

Representation Theory

22 pages, Latex

Scientific paper

It is a basic property of the entropy in statistical physics that is concave as a function of energy. The analog of this in representation theory would be the concavity of the logarithm of the multiplicity of an irreducible representation as a function of its highest weight. We discuss various situations where such concavity can be established or reasonably conjectured and consider some implications of this concavity. These are rather informal notes based on a number of talks I gave on the subject, in particular, at the 1997 International Press lectures at UC Irvine.

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