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- W3025690676 abstract "In 1979, Lusztig proposed a cohomological construction of supercuspidal representations of reductive p-adic groups, analogous to Deligne–Lusztig theory for finite reductive groups. In this paper we establish a new instance of Lusztig’s program. Precisely, let X be the Deligne–Lusztig (ind-pro-)scheme associated to a division algebra D over a non-Archimedean local field K of positive characteristic. We study the $$D^times $$ -representations $$H_bullet (X)$$ by establishing a Deligne–Lusztig theory for families of finite unipotent groups that arise as subquotients of $$D^times $$ . There is a natural correspondence between quasi-characters of the (multiplicative group of the) unramified degree-n extension of K and representations of $$D^{times }$$ given by $$theta mapsto H_bullet (X)[theta ]$$ . For a broad class of characters $$theta ,$$ we show that the representation $$H_bullet (X)[theta ]$$ is irreducible and concentrated in a single degree. After explicitly constructing a Weil representation from $$theta $$ using $$chi $$ -data, we show that the resulting correspondence matches the bijection given by local Langlands and therefore gives a geometric realization of the Jacquet–Langlands transfer between representations of division algebras." @default.
- W3025690676 created "2020-05-21" @default.
- W3025690676 creator A5058333804 @default.
- W3025690676 date "2018-03-29" @default.
- W3025690676 modified "2023-10-18" @default.
- W3025690676 title "Deligne–Lusztig constructions for division algebras and the local Langlands correspondence, II" @default.
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- W3025690676 doi "https://doi.org/10.1007/s00029-018-0410-6" @default.
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