Year: 2025
Type: article
Abstract: We prove that Lusztig’s semi-infinite Deligne–Lusztig variety for $$\textrm{GSp}$$ GSp (and its inner form) is isomorphic, as a set with action, to an affine Deligne–Lusztig variety at infinite level, generalizing a result of Chan–Ivanov. Furthermore, we show that a component of some affine Deligne–Lusztig variety $$X^0_{w_r}(b)_{\mathcal {L}}$$ X w r 0 ( b ) L for $$\textrm{GSp}$$ GSp can be written, up to perfection, as a direct product of a classical Deligne–Lusztig variety with an affine space. We also study the varieties $$X_h$$ X h defined by Chan and Ivanov, and show that $$X_h$$ X h at infinite level can be realized as a subset of semi-infinite Deligne–Lusztig varieties defined using components of affine Deligne–Lusztig varieties such as $$X^0_{w_r}(b)_{\mathcal {L}}$$ X w r 0 ( b ) L above, even in the $$\textrm{GSp}$$ GSp case. This reinterprets previous constructions of representations from $$X_h$$ X h as instances of Lusztig’s conjectural picture.
Source: manuscripta mathematica
Author: Teppei Takamatsu
Institution: Kyoto University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Award: Deligne-Lusztig多様体の局所体類似について
OpenAlex ID: W4416915271