THE POLYTABLOID BASIS EXPANDS POSITIVELY INTO THE WEB BASIS

Abstract

We show that the transition matrix from the polytabloid basis to the web basis of the irreducible $\mathfrak{S}_{2n}$-representation of shape $(n,n)$ has nonnegative integer entries. This proves a conjecture of Russell and Tymoczko [Int. Math. Res. Not., 2019(5) (2019), 1479–1502].

Keywords

• 05E10 (primary)
• 05E40 (secondary)