Vogan classes and cells in the unequal parameter case

TL;DR

This paper extends the known relationship between Vogan classes and cells from the equal parameter case to the more general unequal parameter case, broadening the understanding of their structure.

Contribution

It generalizes Kazhdan and Lusztig's result to the unequal parameter case, providing new insights into the structure of Vogan classes and cells.

Findings

Vogan classes are unions of cells in the unequal parameter case

Extension of Kazhdan and Lusztig's result to a broader setting

Enhanced understanding of the structure of Vogan classes

Abstract

Kazhdan and Lusztig proved that Vogan classes are unions of cells in the equal parameter case. We extend this result in the unequal parameter case.