Jack polynomials and affine Yangian

Abstract

In this paper, we define one kind of new Jack polynomials denoted by Jkλ, which equal the standard Jack polynomials Pλα multiplied by a coefficient. We show that the structure constant Cλμν in Jkλ⋅Jkμ=∑νCλμνJkν can be given from affine Yangian of gl(1). Then we give the Boson-Fermion correspondence for Jack polynomials Jkλ and show that 3-Schur functions Sπ equal Jack polynomials Jkλ in the special case of h1=h, h2=−h−1, h3=−h+h−1.