Moduli of unipotent representations I: Foundational topics

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Abstract

With this work and its sequel, Moduli of unipotent representations II, we initiate a study of the finite dimensional algebraic representations of a unipotent group over a field of characteristic zero from the modular point of view. Let G be such a group. The stack M n(G) of all representations of dimension n is badly behaved. In this first installment, we introduce a nondegeneracy condition which cuts out a substack M n nd(G) which is better behaved, and, in particular, admits a coarse algebraic space, which we denote by M n nd(G). We also study the problem of glueing a pair of nondegenerate representations along a common subquotient.

Original languageEnglish
Pages (from-to)1123-1187
Number of pages65
JournalAnnales de l'Institut Fourier
Volume62
Issue number3
DOIs
StatePublished - 12 Oct 2012
Externally publishedYes

Keywords

  • Coarse moduli space
  • Unipotent group action
  • Unipotent representation

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