Abstract:Gelfand $W$-graphs provide multiplicity-free canonical models for classical Weyl groups, and their molecules record the connectivity generated by bidirected canonical-basis edges. Restricted Beissinger insertion and dual equivalence give a natural tableau language for these edges, while the wall and fork generators require additional local criteria. For both type-$B$ Gelfand $\mathbf m$- and $\mathbf n$-graphs, we prove that the molecules are exactly the connected components of explicit occurrence--wall graphs constructed from split modified Beissinger insertion. In odd type $D$, we likewise classify the $\mathbf m$-molecules by a completion-filtered occurrence--fork graph and obtain the $\mathbf n$-classification through the parity-sensitive type-$D$ duality.
From: Yifeng Zhang [view email]
[v1]
Thu, 30 Nov 2023 06:43:20 UTC (407 KB)
[v2]
Mon, 8 Jan 2024 06:46:49 UTC (33 KB)
[v3]
Sun, 30 Aug 2026 12:54:29 UTC (25 KB)
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