G-complete reducibility in non-connected groups

Michael Bate, Sebastian Herpel, Benjamin Martin, Gerhard Rohrle

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4 Citations (Scopus)
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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 languageEnglish
Pages (from-to)1085-1100
Number of pages16
JournalProceedings of the American Mathematical Society
Issue number3
Early online date12 Nov 2014
Publication statusPublished - Mar 2015

Bibliographical 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.


  • G -complete reducibility
  • non- connected reductive groups


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