The boson-fermion correspondence on (asymmetric) ice

Dr Christian Korff, University of Glasgow. Part of the Algebra, Geometry and Integrable Systems Colloquium.

The boson-fermion correspondence is an important map which plays a key role in representation theory (for example finite dimn’l modules of the symmetric group) and classical integrable systems (the KP hierarchy). In my talk I will show that its extension to the Hecke algebra connects it also to the asymmetric six-vertex model in statistical mechanics which describes ice and other ferroelectrics. Time permitting we will discuss the boson-fermion correspondence also for the cylinder and show that this leads to the definition of an infinite-dimensional coalgebra in the Grothendieck ring of the Hecke algebra whose structure constants are the Gromov-Witten invariants of Grassmannians.