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arXiv · 2605.17844

Recursive structures of molecules and cells in Gelfand $S_n$-graphs

Zhiqiang Dai·Yifeng Zhang
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Abstract

$W$-graphs, representing the multiplication action of the standard basis on the canonical basis in the Iwahori-Hecke algebra are introduced by Kazhdan and Lusztig. Marberg defined a generalized $W$-graph, the Gelfand W-graph, corresponding to the Hecke algebra modules instead of Hecke algebras. To classify the molecules and cells of the Gelfand $S_n$-graphs, in this paper, we introduce a recursive structure of $S_n$ and then discuss the action of the recursive structure on the molecules. Using this structure, we prove that the distinguished nonnesting molecule is a cell.

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Zhiqiang Dai, Yifeng Zhang. 2026-08-12. Recursive structures of molecules and cells in Gelfand $S_n$-graphs. https://arxiv.org/abs/2605.17844

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