Affine Yangian And Schur Functions On Plane Partitions Of 4

In this paper, we first calculate the orthogonal basis of the vector space spanned by e(i)e(j)e(k)e(0)vertical bar 0 >, where e(j) are the generators of the affine Yangian of gl(1). The elements of this orthogonal basis correspond to three dimensional bosons. Then, we calculate the Schur functions of plane partitions of 4, we find that the plane partitions become Young diagrams, and the Schur functions on plane partitions become Schur functions on Young diagrams when h(1) = 1, h(2) = -1, and h(3) = 0. Published under an exclusive license by AIP Publishing.