# Moduli of unipotent representations I: foundational topics

• [1] Leibniz Universität Hannover Institut für Algebra, Zahlentheorie und Diskrete Mathematik Fakultät für Mathematik und Physik Welfengarten 1 30167 Hannover Germany
• Volume: 62, Issue: 3, page 1123-1187
• ISSN: 0373-0956

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## Abstract

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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 ${ℳ}_{n}\left(G\right)$ of all representations of dimension $n$ is badly behaved. In this first installment, we introduce a nondegeneracy condition which cuts out a substack ${ℳ}_{n}^{\mathrm{nd}}\left(G\right)$ which is better behaved, and, in particular, admits a coarse algebraic space, which we denote by ${M}_{n}^{\mathrm{nd}}\left(G\right)$. We also study the problem of glueing a pair of nondegenerate representations along a common subquotient.

## How to cite

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Dan-Cohen, Ishai. "Moduli of unipotent representations I: foundational topics." Annales de l’institut Fourier 62.3 (2012): 1123-1187. <http://eudml.org/doc/251141>.

@article{Dan2012,
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 $\mathcal\{M\}_n(G)$ of all representations of dimension $n$ is badly behaved. In this first installment, we introduce a nondegeneracy condition which cuts out a substack $\mathcal\{M\}_n^\mathrm\{nd\}(G)$ which is better behaved, and, in particular, admits a coarse algebraic space, which we denote by $M_n^\mathrm\{nd\}(G)$. We also study the problem of glueing a pair of nondegenerate representations along a common subquotient.},
affiliation = {Leibniz Universität Hannover Institut für Algebra, Zahlentheorie und Diskrete Mathematik Fakultät für Mathematik und Physik Welfengarten 1 30167 Hannover Germany},
author = {Dan-Cohen, Ishai},
journal = {Annales de l’institut Fourier},
keywords = {unipotent representation; unipotent group action; coarse moduli space; moduli space; nilpotent Lie algebra},
language = {eng},
number = {3},
pages = {1123-1187},
publisher = {Association des Annales de l’institut Fourier},
title = {Moduli of unipotent representations I: foundational topics},
url = {http://eudml.org/doc/251141},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Dan-Cohen, Ishai
TI - Moduli of unipotent representations I: foundational topics
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 3
SP - 1123
EP - 1187
AB - 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 $\mathcal{M}_n(G)$ of all representations of dimension $n$ is badly behaved. In this first installment, we introduce a nondegeneracy condition which cuts out a substack $\mathcal{M}_n^\mathrm{nd}(G)$ which is better behaved, and, in particular, admits a coarse algebraic space, which we denote by $M_n^\mathrm{nd}(G)$. We also study the problem of glueing a pair of nondegenerate representations along a common subquotient.
LA - eng
KW - unipotent representation; unipotent group action; coarse moduli space; moduli space; nilpotent Lie algebra
UR - http://eudml.org/doc/251141
ER -

## References

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