On the derived subgroups of certain unipotent subgroups of reductive groups over infinite fields

C J Bushnell, G Henniart

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8 Citations (Scopus)

Abstract

Let F be an infinite field and G a connected reductive algebraic group defined over F. Let P be a minimal F-parabolic subgroup of G and N the unipotent radical of P. We describe explicitly the derived subgroup N-der of N and prove that its group N-der (F) of F-rational points is precisely the derived subgroup N(F)(der) of the group N(F) of F-rational points of N. This implies a simple description of the maximal abelian quotient of the abstract group N(F). In the case where F is a non-Archimedean local field, this is useful in the theory of generalized Whittaker functions on the locally compact group G(F).
Original languageEnglish
Pages (from-to)211 - 230
Number of pages20
JournalTRANSFORMATION GROUPS
Volume7
Issue number3
DOIs
Publication statusPublished - Sept 2002

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