Base change maps for unipotent algebra groups

dc.creatorBoyarchenko, Mitya
dc.date2006-01-07
dc.date.accessioned2026-07-07T06:58:36Z
dc.date.available2026-07-07T06:58:36Z
dc.descriptionIf A is a finite dimensional nilpotent associative algebra over a finite field k, the set G=1+A of all formal expressions of the form 1+a, where a is an element of A, has a natural group structure, given by (1+a)(1+b)=1+(a+b+ab). A finite group arising in this way is called an algebra group. One can also consider G as a unipotent algebraic group over k. We study representations of G from the point of view of ``geometric character theory'' for algebraic groups over finite fields (cf. G. Lusztig, ``Character sheaves and generalizations'', math.RT/0309134). The main result of this paper is a construction of canonical injective ``base change maps'' between - the set of isomorphism classes of complex irreducible representations of G', and - the set of isomorphism classes of complex irreducible representations of G'', which commute with the natural action of the Galois group Gal(k''/k), where k' is a finite extension of k and k'' is a finite extension of k', and G', G'' are the finite algebra groups obtained from G by extension of scalars.
dc.descriptionLaTeX, 19 pages, all comments are welcome
dc.identifierhttps://arxiv.org/abs/math/0601133
dc.identifierhttp://arxiv.org/abs/math/0601133
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/107421
dc.subjectRepresentation Theory
dc.subjectGroup Theory
dc.titleBase change maps for unipotent algebra groups
dc.typetext

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