Work

THE COHOMOLOGY OF p -ADIC DELIGNE-LUSZTIG SCHEMES OF COXETER TYPE

Year: 2025

Type: article

Abstract: We determine the cohomology of the closed Drinfeld stratum of p -adic Deligne–Lusztig schemes of Coxeter type attached to arbitrary inner forms of unramified groups over a local non-archimedean field. We prove that the corresponding torus weight spaces are supported in exactly one cohomological degree and are pairwise non-isomorphic irreducible representations of the pro-unipotent radical of the corresponding parahoric subgroup. We also prove that all Moy–Prasad quotients of this stratum are maximal varieties, and we investigate the relation between the resulting representations and Kirillov’s orbit method.

Source: Journal of the Institute of Mathematics of Jussieu

DOI: 10.1017/s1474748025000040

Authors: Alexander B. Ivanov, Sian Nie

Institutions: Ruhr University Bochum, Chinese Academy of Sciences, University of Chinese Academy of Sciences

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: Deutsche Forschungsgemeinschaft, National Natural Science Foundation of China