Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions

Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions

We give a criterion which ensures that a group generated by Cartan involutions in the automorph group of a rational quadratic form of signature $(n-1,1)$ is "thin", namely it is of infinite index in the latter. It is based on a graph defined on the integral Cartan root vectors, as well as...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of the European Mathematical Society : JEMS 2014-01, Vol.16 (8), p.1617-1671
Hauptverfasser: Fuchs, Elena, Meiri, Chen, Sarnak, Peter
Format: Artikel
Sprache:eng
Schlagworte:
Group theory and generalizations
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 1671
container_issue 8
container_start_page 1617
container_title Journal of the European Mathematical Society : JEMS
container_volume 16
creator Fuchs, Elena
Meiri, Chen
Sarnak, Peter
description We give a criterion which ensures that a group generated by Cartan involutions in the automorph group of a rational quadratic form of signature $(n-1,1)$ is "thin", namely it is of infinite index in the latter. It is based on a graph defined on the integral Cartan root vectors, as well as Vinberg's theory of hyperbolic reflection groups. The criterion is shown to be robust for showing that many hyperbolic hypergeometric groups for $_nF_{n-1}$ are thin.
doi_str_mv 10.4171/JEMS/471
format Article
fullrecord <record><control><sourceid>ems_cross</sourceid><recordid>TN_cdi_crossref_primary_10_4171_jems_471</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_4171_JEMS_471</sourcerecordid><originalsourceid>FETCH-LOGICAL-c395t-83fa30d5cac827ea186c82ca39a9dc35247044330e9059acc3c8d4fb809956773</originalsourceid><addsrcrecordid>eNo9kF1LwzAUhoMoOKfgT8iFF97UJTtJ01xKmZsyEfy4Llmabi1tUpNW6L-3dbKr8_Ly8HJ4ELql5IFRQRcvq9ePBRP0DM0oAx7JJIbzU-b8El2FUBFCBWcwQ--boTV-5-pS48ZZl3vXDHjvXd8GXDiPu4PBh4nZG9eYzo-c-e5VVzqLlc1xqnynLC7tj6v7qQ3X6KJQdTA3_3eOvp5Wn-km2r6tn9PHbaRB8i5KoFBAcq6VTpbCKJrEY9AKpJK5Br5kgjAGQIwkXCqtQSc5K3YJkZLHQsAc3R93tXcheFNkrS8b5YeMkmxykVWmCdnoYkTvjuhUVK73dnzshE3K_rBf-nJe9A</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions</title><source>European Mathematical Society Publishing House</source><creator>Fuchs, Elena ; Meiri, Chen ; Sarnak, Peter</creator><creatorcontrib>Fuchs, Elena ; Meiri, Chen ; Sarnak, Peter</creatorcontrib><description>We give a criterion which ensures that a group generated by Cartan involutions in the automorph group of a rational quadratic form of signature $(n-1,1)$ is "thin", namely it is of infinite index in the latter. It is based on a graph defined on the integral Cartan root vectors, as well as Vinberg's theory of hyperbolic reflection groups. The criterion is shown to be robust for showing that many hyperbolic hypergeometric groups for $_nF_{n-1}$ are thin.</description><identifier>ISSN: 1435-9855</identifier><identifier>EISSN: 1435-9863</identifier><identifier>DOI: 10.4171/JEMS/471</identifier><language>eng</language><publisher>Zuerich, Switzerland: European Mathematical Society Publishing House</publisher><subject>Group theory and generalizations</subject><ispartof>Journal of the European Mathematical Society : JEMS, 2014-01, Vol.16 (8), p.1617-1671</ispartof><rights>European Mathematical Society</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c395t-83fa30d5cac827ea186c82ca39a9dc35247044330e9059acc3c8d4fb809956773</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>315,781,785,24058,27929,27930</link.rule.ids></links><search><creatorcontrib>Fuchs, Elena</creatorcontrib><creatorcontrib>Meiri, Chen</creatorcontrib><creatorcontrib>Sarnak, Peter</creatorcontrib><title>Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions</title><title>Journal of the European Mathematical Society : JEMS</title><addtitle>J. Eur. Math. Soc</addtitle><description>We give a criterion which ensures that a group generated by Cartan involutions in the automorph group of a rational quadratic form of signature $(n-1,1)$ is "thin", namely it is of infinite index in the latter. It is based on a graph defined on the integral Cartan root vectors, as well as Vinberg's theory of hyperbolic reflection groups. The criterion is shown to be robust for showing that many hyperbolic hypergeometric groups for $_nF_{n-1}$ are thin.</description><subject>Group theory and generalizations</subject><issn>1435-9855</issn><issn>1435-9863</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNo9kF1LwzAUhoMoOKfgT8iFF97UJTtJ01xKmZsyEfy4Llmabi1tUpNW6L-3dbKr8_Ly8HJ4ELql5IFRQRcvq9ePBRP0DM0oAx7JJIbzU-b8El2FUBFCBWcwQ--boTV-5-pS48ZZl3vXDHjvXd8GXDiPu4PBh4nZG9eYzo-c-e5VVzqLlc1xqnynLC7tj6v7qQ3X6KJQdTA3_3eOvp5Wn-km2r6tn9PHbaRB8i5KoFBAcq6VTpbCKJrEY9AKpJK5Br5kgjAGQIwkXCqtQSc5K3YJkZLHQsAc3R93tXcheFNkrS8b5YeMkmxykVWmCdnoYkTvjuhUVK73dnzshE3K_rBf-nJe9A</recordid><startdate>20140101</startdate><enddate>20140101</enddate><creator>Fuchs, Elena</creator><creator>Meiri, Chen</creator><creator>Sarnak, Peter</creator><general>European Mathematical Society Publishing House</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20140101</creationdate><title>Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions</title><author>Fuchs, Elena ; Meiri, Chen ; Sarnak, Peter</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c395t-83fa30d5cac827ea186c82ca39a9dc35247044330e9059acc3c8d4fb809956773</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Group theory and generalizations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Fuchs, Elena</creatorcontrib><creatorcontrib>Meiri, Chen</creatorcontrib><creatorcontrib>Sarnak, Peter</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of the European Mathematical Society : JEMS</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Fuchs, Elena</au><au>Meiri, Chen</au><au>Sarnak, Peter</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions</atitle><jtitle>Journal of the European Mathematical Society : JEMS</jtitle><addtitle>J. Eur. Math. Soc</addtitle><date>2014-01-01</date><risdate>2014</risdate><volume>16</volume><issue>8</issue><spage>1617</spage><epage>1671</epage><pages>1617-1671</pages><issn>1435-9855</issn><eissn>1435-9863</eissn><abstract>We give a criterion which ensures that a group generated by Cartan involutions in the automorph group of a rational quadratic form of signature $(n-1,1)$ is "thin", namely it is of infinite index in the latter. It is based on a graph defined on the integral Cartan root vectors, as well as Vinberg's theory of hyperbolic reflection groups. The criterion is shown to be robust for showing that many hyperbolic hypergeometric groups for $_nF_{n-1}$ are thin.</abstract><cop>Zuerich, Switzerland</cop><pub>European Mathematical Society Publishing House</pub><doi>10.4171/JEMS/471</doi><tpages>55</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 1435-9855
ispartof Journal of the European Mathematical Society : JEMS, 2014-01, Vol.16 (8), p.1617-1671
issn 1435-9855
1435-9863
language eng
recordid cdi_crossref_primary_10_4171_jems_471
source European Mathematical Society Publishing House
subjects Group theory and generalizations
title Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-16T09%3A54%3A09IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-ems_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Hyperbolic%20monodromy%20groups%20for%20the%20hypergeometric%20equation%20and%20Cartan%20involutions&rft.jtitle=Journal%20of%20the%20European%20Mathematical%20Society%20:%20JEMS&rft.au=Fuchs,%20Elena&rft.date=2014-01-01&rft.volume=16&rft.issue=8&rft.spage=1617&rft.epage=1671&rft.pages=1617-1671&rft.issn=1435-9855&rft.eissn=1435-9863&rft_id=info:doi/10.4171/JEMS/471&rft_dat=%3Cems_cross%3E10_4171_JEMS_471%3C/ems_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true