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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Integral structures in the $p$-adic holomorphic discrete series
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by Elmar Grosse-Klönne
Represent. Theory 9 (2005), 354-384
Published electronically: April 19, 2005


For a local non-Archimedean field $K$ we construct ${\mathrm {GL}}_{d+1}(K)$-equivariant coherent sheaves ${\mathcal V}_{{\mathcal O}_K}$ on the formal ${\mathcal O}_K$-scheme ${\mathfrak X}$ underlying the symmetric space $X$ over $K$ of dimension $d$. These ${\mathcal V}_{{\mathcal O}_K}$ are ${\mathcal O}_K$-lattices in (the sheaf version of) the holomorphic discrete series representations (in $K$-vector spaces) of ${\mathrm {GL}}_{d+1}(K)$ as defined by P. Schneider. We prove that the cohomology $H^t({\mathfrak X},{\mathcal V}_{{\mathcal O}_K})$ vanishes for $t>0$, for ${\mathcal V}_{{\mathcal O}_K}$ in a certain subclass. The proof is related to the other main topic of this paper: over a finite field $k$, the study of the cohomology of vector bundles on the natural normal crossings compactification $Y$ of the Deligne-Lusztig variety $Y^0$ for ${\mathrm {GL}}_{d+1}/k$ (so $Y^0$ is the open subscheme of ${\mathbb P}_k^d$ obtained by deleting all its $k$-rational hyperplanes).
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Bibliographic Information
  • Elmar Grosse-Klönne
  • Affiliation: Mathematisches Institut der Universität Münster, Einsteinstrasse 62, 48149 Münster, Germany
  • Email:
  • Received by editor(s): October 2, 2004
  • Received by editor(s) in revised form: March 5, 2005
  • Published electronically: April 19, 2005
  • © Copyright 2005 American Mathematical Society
  • Journal: Represent. Theory 9 (2005), 354-384
  • MSC (2000): Primary 14G22
  • DOI:
  • MathSciNet review: 2133764