Abstract

Inspired by Okounkov's work (2001) [20] which relates KP hierarchy to determinant point process, we establish a relationship between BKP hierarchy and Pfaffian point process. We prove that the correlation function of the shifted Schur measures on strict partitions can be expressed as a Pfaffian of skew symmetric matrix kernel, whose elements are certain vacuum expectations of neutral fermions. We further show that the matrix integrals solution of BKP hierarchy can also induce a certain Pfaffian point process.

Highlights

  • There is a connection revealed by Okounkov [20] between random partitions and KP hierarchy of type A∞

  • The correlation function can be realized as a determinant point process via the Fock space formalism, which satisfies the KP hierarchy

  • The tau function can be viewed as an element in the Bosonic Fock space, and it can be expressed in terms of Schur funcions

Read more

Summary

Introduction

There is a connection revealed by Okounkov [20] between random partitions and KP hierarchy of type A∞. As the BKP tau functions can be described respectively in the Bosonic picture and the Fermionic picture [31], the Boson-Fermion correspondence of type B∞ allows us to relate projective Schur functions to vacuum expectations of neutral fermions. Inspired by these facts, we generalize Okounkov’s results to BKP hierarchy in this paper.

A brief introduction to neutral fermions
Schur Q-functions and Pfaffian point process
Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call