Determination of Socle Series using the Condensation Method
Identifieur interne : 001030 ( Istex/Corpus ); précédent : 001029; suivant : 001031Determination of Socle Series using the Condensation Method
Auteurs : Klaus Lux ; Markus WiegelmannSource :
- Journal of Symbolic Computation [ 0747-7171 ] ; 2001.
Abstract
We show how the condensation method introduced by R. A. Parker can be applied to determine the socle series of a finite-dimensional representation of a group over a finite field. We develop several new techniques for this approach and illustrate their power by the example of the socle series of all projective indecomposable representations of the sporadic simple Mathieu group M23in characteristic 2.
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DOI: 10.1006/jsco.1999.1009
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Austr. Math. Soc. A</title></host><title>Testing modules for irreducibility</title></json:item><json:item><author><json:item><name>G.D James</name></json:item></author><host><volume>27</volume><pages><last>111</last><first>57</first></pages><author></author><title>J. Algebra</title></host><title>The modular characters of the Mathieu groups</title></json:item><json:item><host><author></author><title>An Atlas of Brauer Characters</title></host></json:item><json:item><host><author></author><title>Finite Group Algebras and their Modules</title></host></json:item><json:item><author><json:item><name>K Lux</name></json:item><json:item><name>J Müller</name></json:item><json:item><name>M Ringe</name></json:item></author><host><volume>17</volume><pages><last>544</last><first>529</first></pages><author></author><title>J. Symb. Comput.</title></host><title>Peakword condensation and submodule lattices: an application of the MeatAxe</title></json:item><json:item><author><json:item><name>K Lux</name></json:item><json:item><name>M Wiegelmann</name></json:item></author><host><author></author><title>The Atlas, Ten Years On</title></host><title>Condensing tensor product modules</title></json:item><json:item><author><json:item><name>R.A Parker</name></json:item></author><host><pages><last>274</last><first>267</first></pages><author></author><title>Computational Group, Theory</title></host><title>The computer calculation of modular characters (the MeatAxe)</title></json:item><json:item><host><author></author><title>The C-MeatAxe, Release 2.2.0</title></host></json:item><json:item><host><author></author><title>GAP—Groups, Algorithms and Programming, 3.4 edn</title></host></json:item><json:item><host><author></author></host></json:item><json:item><host><author></author><title>G-Algebras and Modular Representation Theory</title></host></json:item><json:item><host><author></author></host></json:item></refBibs><genre><json:string>research-article</json:string></genre><host><volume>31</volume><pii><json:string>S0747-7171(00)X0013-2</json:string></pii><pages><last>178</last><first>163</first></pages><issn><json:string>0747-7171</json:string></issn><issue>1–2</issue><genre><json:string>journal</json:string></genre><language><json:string>unknown</json:string></language><title>Journal of Symbolic Computation</title><publicationDate>2001</publicationDate></host><categories><wos><json:string>science</json:string><json:string>mathematics, applied</json:string><json:string>computer science, theory & methods</json:string></wos><scienceMetrix><json:string>natural sciences</json:string><json:string>mathematics & statistics</json:string><json:string>general mathematics</json:string></scienceMetrix></categories><publicationDate>2001</publicationDate><copyrightDate>2001</copyrightDate><doi><json:string>10.1006/jsco.1999.1009</json:string></doi><id>6FA83BB1199BF508039AE38D82261F721F5A7358</id><score>0.5990275</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/6FA83BB1199BF508039AE38D82261F721F5A7358/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/6FA83BB1199BF508039AE38D82261F721F5A7358/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/6FA83BB1199BF508039AE38D82261F721F5A7358/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a" type="main" xml:lang="en">Determination of Socle Series using the Condensation Method</title></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>ELSEVIER</publisher><availability><p>©2001 Academic Press</p></availability><date>2001</date></publicationStmt><notesStmt><note type="content">Section title: Regular Article</note></notesStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">Determination of Socle Series using the Condensation Method</title><author xml:id="author-1"><persName><forename type="first">Klaus</forename><surname>Lux</surname></persName><note type="biography">Email: klux@math.rwth-aachen.de</note><affiliation>Email: klux@math.rwth-aachen.de</affiliation><affiliation>Lehrstuhl D für Mathematik, RWTH Aachen, Templergraben 55, D-52062, Aachen, Germany</affiliation></author><author xml:id="author-2"><persName><forename type="first">Markus</forename><surname>Wiegelmann</surname></persName><note type="biography">Email: wiegelm@uni-trier.de</note><affiliation>Email: wiegelm@uni-trier.de</affiliation><affiliation>Fachbereich Mathematik, Universität Trier, Universitästring 15, D-54286, Trier, Germany</affiliation></author></analytic><monogr><title level="j">Journal of Symbolic Computation</title><title level="j" type="abbrev">YJSCO</title><idno type="pISSN">0747-7171</idno><idno type="PII">S0747-7171(00)X0013-2</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="2001"></date><biblScope unit="volume">31</biblScope><biblScope unit="issue">1–2</biblScope><biblScope unit="page" from="163">163</biblScope><biblScope unit="page" to="178">178</biblScope></imprint></monogr><idno type="istex">6FA83BB1199BF508039AE38D82261F721F5A7358</idno><idno type="DOI">10.1006/jsco.1999.1009</idno><idno type="PII">S0747-7171(99)91009-X</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2001</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>We show how the condensation method introduced by R. 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A. Parker can be applied to determine the socle series of a finite-dimensional representation of a group over a finite field. We develop several new techniques for this approach and illustrate their power by the example of the socle series of all projective indecomposable representations of the sporadic simple Mathieu group <ce:italic>M</ce:italic><ce:inf>23</ce:inf>in characteristic 2.</ce:simple-para></ce:abstract-sec></ce:abstract></head></converted-article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Determination of Socle Series using the Condensation Method</title></titleInfo><titleInfo type="alternative" lang="en" contentType="CDATA"><title>Determination of Socle Series using the Condensation Method</title></titleInfo><name type="personal"><namePart type="given">Klaus</namePart><namePart type="family">Lux</namePart><affiliation>Lehrstuhl D für Mathematik, RWTH Aachen, Templergraben 55, D-52062, Aachen, Germany</affiliation><description>Email: klux@math.rwth-aachen.de</description><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Markus</namePart><namePart type="family">Wiegelmann</namePart><affiliation>Fachbereich Mathematik, Universität Trier, Universitästring 15, D-54286, Trier, Germany</affiliation><description>Email: wiegelm@uni-trier.de</description><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="Full-length article"></genre><originInfo><publisher>ELSEVIER</publisher><dateIssued encoding="w3cdtf">2001</dateIssued><copyrightDate encoding="w3cdtf">2001</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">We show how the condensation method introduced by R. A. Parker can be applied to determine the socle series of a finite-dimensional representation of a group over a finite field. 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