Forum of Mathematics, Sigma (Jan 2024)

Orthogonality relations for deep level Deligne–Lusztig schemes of Coxeter type

  • Olivier Dudas,
  • Alexander B. Ivanov

DOI
https://doi.org/10.1017/fms.2024.55
Journal volume & issue
Vol. 12

Abstract

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In this paper, we prove some orthogonality relations for representations arising from deep level Deligne–Lusztig schemes of Coxeter type. This generalizes previous results of Lusztig [Lus04], and of Chan and the second author [CI21b]. Applications include the study of smooth representations of p-adic groups in the cohomology of p-adic Deligne–Lusztig spaces and their relation to the local Langlands correspondences. Also, the geometry of deep level Deligne–Lusztig schemes gets accessible, in the spirit of Lusztig’s work [Lus76].

Keywords