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 language | English |
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Pages (from-to) | 211 - 230 |
Number of pages | 20 |
Journal | TRANSFORMATION GROUPS |
Volume | 7 |
Issue number | 3 |
DOIs | |
Publication status | Published - Sept 2002 |