G-complete reducibility in non-connected groups

Michael Bate; Sebastian Herpel; Benjamin Martin; Gerhard Rohrle

doi:10.1090/S0002-9939-2014-12348-3

G-complete reducibility in non-connected groups

Michael Bate, Sebastian Herpel, Benjamin Martin, Gerhard Rohrle

Mathematical Science

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3 Citations (Scopus)

4 Downloads (Pure)

Abstract

In this paper we present an algorithm for determining whether a subgroup H of a non-connected reductive group G is G-completely reducible. The algorithm consists of a series of reductions; at each step, we perform operations involving connected groups, such as checking whether a certain subgroup of G⁰ is G⁰-cr. This essentially reduces the problem of determining G-complete reducibility to the connected case.

Original language	English
Pages (from-to)	1085-1100
Number of pages	16
Journal	Proceedings of the American Mathematical Society
Volume	143
Issue number	3
Early online date	12 Nov 2014
DOIs	https://doi.org/10.1090/S0002-9939-2014-12348-3
Publication status	Published - Mar 2015

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Keywords

G -complete reducibility
non- connected reductive groups

Cite this

Bate, M., Herpel, S., Martin, B., & Rohrle, G. (2015). G-complete reducibility in non-connected groups. Proceedings of the American Mathematical Society, 143(3), 1085-1100. https://doi.org/10.1090/S0002-9939-2014-12348-3

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abstract = "In this paper we present an algorithm for determining whether a subgroup H of a non-connected reductive group G is G-completely reducible. The algorithm consists of a series of reductions; at each step, we perform operations involving connected groups, such as checking whether a certain subgroup of G0 is G0-cr. This essentially reduces the problem of determining G-complete reducibility to the connected case.",

keywords = "G -complete reducibility, non- connected reductive groups",

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note = "The authors acknowledge the financial support of the DFG-priority programme SPP1388 “Representation Theory” and Marsden Grants UOC0501, UOC1009 and UOA1021. Part of the research for this paper was carried out while the authors were staying at the Mathematical Research Institute Oberwolfach supported by the “Research in Pairs” programme. The second author acknowledges additional support from ERC Advanced Grant No. 291512. The authors are grateful to the referee for helpful suggestions, including a strengthening of Proposition 3.4.",

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10.1090/S0002-9939-2014-12348-3Licence: Unspecified

Accepted Manuscript
©2014 American Mathematical Society. First published in Proceedings of the American Mathematical Society 143 (2015), 1085-1100, published by the American Mathematical Society.
Accepted author manuscript, 381 KBLicence: Other

http://www.ams.org/publications/ctp.pdf