Positive temperature free fermions and solvable models in the KPZ class
Matteo Mucciconi
Mathematics Institute, University of Warwick
Lundi 07/03/2022, 11:00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
During the last two decades the study of solvable stochastic systems in the KPZ universality class has attracted much attention. A typical feature of these solvable models is their connection with special symmetric polynomials, which characterize their probability distribution. In numerous cases, utilizing Macdonald difference operators or Bethe Ansatz, one point functions have been expressed in the form of Fredholm determinants or pfaffians, leading to precise asymptotic analysis. In this talk we aim to describe the origin of such determinantal and pfaffian formulas, relating the theory of solvable KPZ models with that of positive temperature free fermions in one dimension. We accomplish this by establishing new identities between restricted Cauchy sums of skew Schur polynomials and q-Whittaker polynomials (i.e. Macdonald polynomials with t=0). This result is a consequence of a new bijective q-deformation of the celebrated RSK correspondence we introduce. Our arguments pivot around a combination of various theories that include Kirillov-Reshetikhin crystals, Demazure modules and the Box-Ball system. This is a joint work with Takashi Imamura and Tomohiro Sasamoto.
Contact : Jeremie BOUTTIER


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