2023/06/24 by Knutson, Allen, Zinn-Justin, Paul · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2306.13855
In paper I of this series we gave positive formulae for expanding the product \mathfrak Sπ\mathfrak Sρ of two Schubert polynomials, in the case that both π,ρ had shared descent set of size ≤ 3. Here we introduce and give positive formulae for two new classes of Schubert product problems: separated descent in which π's last descent occurs at (or before) ρ's first, and almost separated descent in which π's last two descents occur at (or before) ρ's first two respectively. In both cases our puzzle formulae extend to K-theory (multiplying Grothendieck polynomials), and in the separated descent case, to equivariant K-theory. The two formulae arise (via quantum integrability) from fusion of minuscule quantized loop algebra representations in types A, D respectively.