Publications

We introduce the immersion poset (P(n),⩽I) on partitions, defined by λ⩽Iμ if and only if sμ(x1,…,xN)-sλ(x1,…,xN) is monomial-positive. Relations in the immersion poset determine when irreducible polynomial representations of GLN(C) form an immersion pair, as defined by Prasad and Raghunathan [7]. We develop injections SSYT(λ,ν)↪SSYT(μ,ν) on semistandard Young tableaux given constraints on the shape of λ, and present results on immersion relations among hook and two column partitions. The standard immersion poset (P(n),⩽std) is a refinement of the immersion poset, defined by λ⩽stdμ if and only if λ⩽Dμ in dominance order and fλ⩽fμ, where fν is the number of standard Young tableaux of shape ν. We classify maximal elements of certain shapes in the standard immersion poset using the hook length formula. Finally, we prove Schur-positivity of power sum symmetric functions on conjectured lower intervals in the immersion poset, addressing questions posed by Sundaram [12].