A combinatorial model for the transition matrix between the Specht and $\operatorname {SL}_2$-web bases
Forum of Mathematics, Sigma, Tome 11 (2023)
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We introduce a new class of permutations, called web permutations. Using these permutations, we provide a combinatorial interpretation for entries of the transition matrix between the Specht and $\operatorname {SL}_2$-web bases of the irreducible $ \mathfrak {S}_{2n} $-representation indexed by $ (n,n) $, which answers Rhoades’s question. Furthermore, we study enumerative properties of these permutations.
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author = {Byung-Hak Hwang and Jihyeug Jang and Jaeseong Oh},
title = {A combinatorial model for the transition matrix between the {Specht} and $\operatorname {SL}_2$-web bases},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {11},
year = {2023},
doi = {10.1017/fms.2023.79},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.79/}
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AU - Jihyeug Jang
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Byung-Hak Hwang; Jihyeug Jang; Jaeseong Oh. A combinatorial model for the transition matrix between the Specht and $\operatorname {SL}_2$-web bases. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.79
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