2025/11/02 by Graf, John
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2511.01114
The Bernstein operator Bn acts on a Schur function Sλ by appending a part to the index, i.e., Bn Sλ=S(n,λ). This provides a method of constructing the vertex operator representation of Schur functions since its homogeneous components are essentially just these Bernstein operators. Meanwhile, the Hall-Littlewood functions are an important generalization of the Schur functions, and they also have a vertex operator representation due to Jing. In this paper, we construct a t-analogue of the Bernstein operator, which allows for an explicit construction of the Jing operator. We show that the usual involution ω is fundamental to this construction, revealing further combinatorial structure. As an application, we use this vertex operator to prove stability of certain structure coefficients, including the Hall polynomials.