117 citations · 248 across the 15 of their papers we have counts for
4 papers · 1 filter
Combinatorial formula for Macdonald polynomials, Bethe Ansatz, and generic Macdonald polynomials
Andrei Okounkov
We give a direct proof of the combinatorial formula for interpolation Macdonald polynomials by introducing certain polynomials, which we call generic Macdonald polynomials, which d…
Toda equations for Hurwitz numbers
Andrei Okounkov
We consider ramified coverings of P^1 with arbitrary ramification type over 0 and infinity and simple ramifications elsewhere and prove that the generating function for the numbers…
SL(2) and z-measures
Andrei Okounkov
We give a representation-theoretic proof of the formula for correlation functions of z-measures obtained by Borodin and Olshanski in math.RT/9904010. This paper is historically pre…
Why would multiplicities be log-concave ?
Andrei Okounkov
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 loga…