THE POLYTABLOID BASIS EXPANDS POSITIVELY INTO THE WEB BASIS
Forum of Mathematics, Sigma, Tome 7 (2019)
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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].
@article{10_1017_fms_2019_22,
author = {BRENDON RHOADES},
title = {THE {POLYTABLOID} {BASIS} {EXPANDS} {POSITIVELY} {INTO} {THE} {WEB} {BASIS}},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {7},
year = {2019},
doi = {10.1017/fms.2019.22},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2019.22/}
}
BRENDON RHOADES. THE POLYTABLOID BASIS EXPANDS POSITIVELY INTO THE WEB BASIS. Forum of Mathematics, Sigma, Tome 7 (2019). doi: 10.1017/fms.2019.22
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