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Mathematics > Representation Theory

arXiv:math/0002085 (math)
[Submitted on 11 Feb 2000]

Title:Why would multiplicities be log-concave ?

Authors:Andrei Okounkov
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Abstract: 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.
Comments: 22 pages, Latex
Subjects: Representation Theory (math.RT); Mathematical Physics (math-ph); Algebraic Geometry (math.AG); Combinatorics (math.CO)
Cite as: arXiv:math/0002085 [math.RT]
  (or arXiv:math/0002085v1 [math.RT] for this version)
  https://doi.org/10.48550/arXiv.math/0002085

Submission history

From: Andrei Okounkov [view email]
[v1] Fri, 11 Feb 2000 00:40:07 UTC (15 KB)
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