Cell Classification of Gelfand $S_n$-Graphs
Combinatorics
2026-04-06 v4 Representation Theory
Abstract
Kazhdan and Lusztig introduced the -graphs, which represent the multiplication action of the standard basis on the canonical bais in the Iwahori-Hecke algebra. In the Hecke algebra module, Marberg defined two generalied -graphs, called the Gelfand -graphs. The classification of the molecules of the type Gelfand -graphs are determined by two RSK-like insertion algorithms. We finish the classification of cells by proving that every molecule in the -graphs is indeed a cell.
Cite
@article{arxiv.2503.21215,
title = {Cell Classification of Gelfand $S_n$-Graphs},
author = {Yifeng Zhang},
journal= {arXiv preprint arXiv:2503.21215},
year = {2026}
}
Comments
28 pages. arXiv admin note: text overlap with arXiv:2412.07810