Year: 2024
Type: preprint
Abstract: In this paper, we formulate the notion of split elements of a unipotent class in a connected reductive group $G$. Generalized Green functions of $G$ can be computed by using Lusztig's algorithm, if split elements exist for any unipotent class. The existence of split elements is reduced to the case where $G$ is a simply connected, almost simple group. We show, in the case of classical groups, split elements exist, which is a refinement of previous results. In the case of exceptional groups, we show the existence of split elements, possibly except one class for $G$ of type $E_7$.
Source: arXiv (Cornell University)
Authors: Lübeck, Frank, Shoji, Toshiaki
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4402951256