3D Fermion representation of affine Yangian

Abstract

In this paper, we give the 3D (3 dimensional) Fermion representation of affine Yangian of gl(1). In special case h1=1,h2=−1,h3=0, the 3D Fermion operators Γm→ and Γm→⁎ become γm→ and γm→⁎ which have relations with 2D Fermions. By Boson-Fermion correspondence, we obtain that the Schur operators Sˆλ are functions of γm→, which give an explicit description for Littlewood-Richardson rule.