On irreducible subgroups of simple algebraic groups
Let G be a simple algebraic group over an algebraically closed field K of characteristic p ⩾ 0 , let H be a proper closed subgroup of G and let V be a nontrivial irreducible KG -module, which is p -restricted, tensor indecomposable and rational. Assume that the restriction of V to H is irreducible....
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| Veröffentlicht in: | Mathematische annalen 2017-04, Vol.367 (3-4), p.1259-1309 |
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| container_title | Mathematische annalen |
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| creator | Burness, Timothy C. Marion, Claude Testerman, Donna M. |
| description | Let
G
be a simple algebraic group over an algebraically closed field
K
of characteristic
p
⩾
0
, let
H
be a proper closed subgroup of
G
and let
V
be a nontrivial irreducible
KG
-module, which is
p
-restricted, tensor indecomposable and rational. Assume that the restriction of
V
to
H
is irreducible. In this paper, we study the triples (
G
,
H
,
V
) of this form when
G
is a classical group and
H
is positive-dimensional. Combined with earlier work of Dynkin, Seitz, Testerman and others, our main theorem reduces the problem of classifying the triples (
G
,
H
,
V
) to the case where
G
is an orthogonal group,
V
is a spin module and
H
normalizes an orthogonal decomposition of the natural
KG
-module. |
| doi_str_mv | 10.1007/s00208-016-1432-z |
| format | Article |
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G
be a simple algebraic group over an algebraically closed field
K
of characteristic
p
⩾
0
, let
H
be a proper closed subgroup of
G
and let
V
be a nontrivial irreducible
KG
-module, which is
p
-restricted, tensor indecomposable and rational. Assume that the restriction of
V
to
H
is irreducible. In this paper, we study the triples (
G
,
H
,
V
) of this form when
G
is a classical group and
H
is positive-dimensional. Combined with earlier work of Dynkin, Seitz, Testerman and others, our main theorem reduces the problem of classifying the triples (
G
,
H
,
V
) to the case where
G
is an orthogonal group,
V
is a spin module and
H
normalizes an orthogonal decomposition of the natural
KG
-module.</description><identifier>ISSN: 0025-5831</identifier><identifier>EISSN: 1432-1807</identifier><identifier>DOI: 10.1007/s00208-016-1432-z</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Algebra ; Group theory ; Mathematics ; Mathematics and Statistics ; Subgroups</subject><ispartof>Mathematische annalen, 2017-04, Vol.367 (3-4), p.1259-1309</ispartof><rights>The Author(s) 2016</rights><rights>Copyright Springer Science & Business Media 2017</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c359t-2b42ab14e5e669ce2c1d24c1ca95c22bd6ae78dc0510acf2738c8d6ed1ea58743</citedby><cites>FETCH-LOGICAL-c359t-2b42ab14e5e669ce2c1d24c1ca95c22bd6ae78dc0510acf2738c8d6ed1ea58743</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00208-016-1432-z$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00208-016-1432-z$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Burness, Timothy C.</creatorcontrib><creatorcontrib>Marion, Claude</creatorcontrib><creatorcontrib>Testerman, Donna M.</creatorcontrib><title>On irreducible subgroups of simple algebraic groups</title><title>Mathematische annalen</title><addtitle>Math. Ann</addtitle><description>Let
G
be a simple algebraic group over an algebraically closed field
K
of characteristic
p
⩾
0
, let
H
be a proper closed subgroup of
G
and let
V
be a nontrivial irreducible
KG
-module, which is
p
-restricted, tensor indecomposable and rational. Assume that the restriction of
V
to
H
is irreducible. In this paper, we study the triples (
G
,
H
,
V
) of this form when
G
is a classical group and
H
is positive-dimensional. Combined with earlier work of Dynkin, Seitz, Testerman and others, our main theorem reduces the problem of classifying the triples (
G
,
H
,
V
) to the case where
G
is an orthogonal group,
V
is a spin module and
H
normalizes an orthogonal decomposition of the natural
KG
-module.</description><subject>Algebra</subject><subject>Group theory</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Subgroups</subject><issn>0025-5831</issn><issn>1432-1807</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp1kE1PwzAMhiMEEmPwA7hV4hyw89FmRzTxJU3aBc5RmrpVp64tyXpgv56McuDCyZbf97Xlh7FbhHsEKB4igADDAXOOSgp-PGOLnwYNFOdskWTNtZF4ya5i3AGABNALJrd91oZA1eTbsqMsTmUThmmM2VBnsd2Paea6hsrgWp_N0jW7qF0X6ea3LtnH89P7-pVvti9v68cN91KvDlyUSrgSFWnK85Un4bESyqN3K-2FKKvcUWEqDxrB-VoU0nhT5VQhOW0KJZfsbt47huFzoniwu2EKfTpp0aS3lM4VJBfOLh-GGAPVdgzt3oUvi2BPbOzMxiY29oTEHlNGzJmYvH1D4c_mf0PfQ8tnDQ</recordid><startdate>20170401</startdate><enddate>20170401</enddate><creator>Burness, Timothy C.</creator><creator>Marion, Claude</creator><creator>Testerman, Donna M.</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20170401</creationdate><title>On irreducible subgroups of simple algebraic groups</title><author>Burness, Timothy C. ; Marion, Claude ; Testerman, Donna M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c359t-2b42ab14e5e669ce2c1d24c1ca95c22bd6ae78dc0510acf2738c8d6ed1ea58743</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Algebra</topic><topic>Group theory</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Subgroups</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Burness, Timothy C.</creatorcontrib><creatorcontrib>Marion, Claude</creatorcontrib><creatorcontrib>Testerman, Donna M.</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><jtitle>Mathematische annalen</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Burness, Timothy C.</au><au>Marion, Claude</au><au>Testerman, Donna M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On irreducible subgroups of simple algebraic groups</atitle><jtitle>Mathematische annalen</jtitle><stitle>Math. Ann</stitle><date>2017-04-01</date><risdate>2017</risdate><volume>367</volume><issue>3-4</issue><spage>1259</spage><epage>1309</epage><pages>1259-1309</pages><issn>0025-5831</issn><eissn>1432-1807</eissn><abstract>Let
G
be a simple algebraic group over an algebraically closed field
K
of characteristic
p
⩾
0
, let
H
be a proper closed subgroup of
G
and let
V
be a nontrivial irreducible
KG
-module, which is
p
-restricted, tensor indecomposable and rational. Assume that the restriction of
V
to
H
is irreducible. In this paper, we study the triples (
G
,
H
,
V
) of this form when
G
is a classical group and
H
is positive-dimensional. Combined with earlier work of Dynkin, Seitz, Testerman and others, our main theorem reduces the problem of classifying the triples (
G
,
H
,
V
) to the case where
G
is an orthogonal group,
V
is a spin module and
H
normalizes an orthogonal decomposition of the natural
KG
-module.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00208-016-1432-z</doi><tpages>51</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0025-5831 |
| ispartof | Mathematische annalen, 2017-04, Vol.367 (3-4), p.1259-1309 |
| issn | 0025-5831 1432-1807 |
| language | eng |
| recordid | cdi_proquest_journals_1880745640 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Algebra Group theory Mathematics Mathematics and Statistics Subgroups |
| title | On irreducible subgroups of simple algebraic groups |
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