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arXiv · 2412.07810

Lusztig $\mathbf{a}$-functions for quasiparabolic sets

Yifeng Zhang
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Abstract

Kazhdan and Lusztig introduce the $W$-graphs to describe the cells and molecules corresponding to the Coxeter groups. Building on this foundation, Lusztig defines the a-funtion to classify the cells, as well as the molecules. Marberg then generalizes Kazhdan and Lusztig's $W$-graphs, using fixed-point-free involutions as their indices. The molecules of the two new $S_n$-graphs are then classified via two correspondence similar to RSK correspondence by Marberg and me. In this paper, we define an analogue of the Lusztig a-function and finish the classification of cells by proving that every molecule in the $S_n$-graphs is indeed a cell.

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Yifeng Zhang. 2024-12-10. Lusztig $\mathbf{a}$-functions for quasiparabolic sets. https://arxiv.org/abs/2412.07810

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