Why would multiplicities be log-concave ?
Okounkov, Andrei
arXiv, 0002085 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2000-02-10
Classification:  Mathematics - Representation Theory,  Mathematical Physics,  Mathematics - Algebraic Geometry,  Mathematics - Combinatorics 
@article{0002085,
     author = {Okounkov, Andrei},
     title = {Why would multiplicities be log-concave ?},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0002085}
}

Okounkov, Andrei. Why would multiplicities be log-concave ?. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0002085/