On irreducibility of tensor products of Yangian modules associated with skew Young diagrams

We study the tensor product $W$ of any number of irreducible finite-dimensional modules $V\sb 1,\ldots V\sb k$ over the Yangian ${\rm Y}(\mathfrak {gl}\sb N)$ of the general linear Lie algebra $\mathfrak {gl}\sb N$. For any indices $i,j=1,\ldots k$, there is a canonical nonzero intertwining operator...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Duke mathematical journal 2002-04, Vol.112 (2), p.343-378
Hauptverfasser:	Nazarov, Maxim, Tarasov, Vitaly
Format:	Artikel
Sprache:	eng
Schlagworte:	17B37 20G42 81R50 82B23 Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

container_end_page	378
container_issue	2
container_start_page	343
container_title	Duke mathematical journal
container_volume	112
creator	Nazarov, Maxim Tarasov, Vitaly
description	We study the tensor product $W$ of any number of irreducible finite-dimensional modules $V\sb 1,\ldots V\sb k$ over the Yangian ${\rm Y}(\mathfrak {gl}\sb N)$ of the general linear Lie algebra $\mathfrak {gl}\sb N$. For any indices $i,j=1,\ldots k$, there is a canonical nonzero intertwining operator $J\sb {ij} : V\sb i\otimes V\sb j\to V\sb j\otimes V\sb i$. It has been conjectured that the tensor product $W$ is irreducible if and only if all operators $J\sb {ij}$ with $i
doi_str_mv	10.1215/S0012-9074-02-11225-3
format	Article
fullrecord	<record><control><sourceid>istex_proje</sourceid><recordid>TN_cdi_projecteuclid_primary_oai_CULeuclid_euclid_dmj_1087575155</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>ark_67375_765_KFB3ZPWH_1</sourcerecordid><originalsourceid>FETCH-LOGICAL-c346t-7ea4bee1c11bedbb05b1046a31e5ff750bf84412b4e03646b5e51d369bff92403</originalsourceid><addsrcrecordid>eNo9kNtKAzEQhoMoWKuPIOQFopkcNt07tagVCxVURL0Iye5sTQ-7Jdmivr3bA14N8zPfz_ARcg78AgToy2fOQbCcG8W4YABCaCYPSA-0MszIfHBIetsTw3N1TE5Smm3WPBM98jmpaYgRy3URfFiE9pc2FW2xTk2kq9h0eZs20burp8HVdNlFC0zUpdQUwbVY0u_QftE0x2_63qzrKS2Dm0a3TKfkqHKLhGf72Sevd7cvwxEbT-4fhtdjVkiVtcygUx4RCgCPpfdce-AqcxJQV5XR3FcDpUB4hVxmKvMaNZQyy31V5UJx2SdXu97u3xkWLa6LRSjtKoali7-2ccEOX8f7dD_K5cwCHxhtNGjdVehdRRGblCJW_zRwu5Fst5LtRrLlwm4lW9lxbMeF1OLPP-Ti3GZGGm1Npu3j3Y38eHobWZB_cESBKw</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>On irreducibility of tensor products of Yangian modules associated with skew Young diagrams</title><source>Project Euclid Complete</source><creator>Nazarov, Maxim ; Tarasov, Vitaly</creator><creatorcontrib>Nazarov, Maxim ; Tarasov, Vitaly</creatorcontrib><description>We study the tensor product $W$ of any number of irreducible finite-dimensional modules $V\sb 1,\ldots V\sb k$ over the Yangian ${\rm Y}(\mathfrak {gl}\sb N)$ of the general linear Lie algebra $\mathfrak {gl}\sb N$. For any indices $i,j=1,\ldots k$, there is a canonical nonzero intertwining operator $J\sb {ij} : V\sb i\otimes V\sb j\to V\sb j\otimes V\sb i$. It has been conjectured that the tensor product $W$ is irreducible if and only if all operators $J\sb {ij}$ with $i<j$ are invertible. We prove this conjecture for a wide class of irreducible ${\rm Y}(\mathfrak {gl}\sb N)$-modules $V\sb 1,\ldots V\sb k$. Each of these modules is determined by a skew Young diagram and a complex parameter. We also introduce the notion of a Durfee rank of a skew Young diagram. For an ordinary Young diagram, this is the length of its main diagonal.</description><identifier>ISSN: 0012-7094</identifier><identifier>EISSN: 1547-7398</identifier><identifier>DOI: 10.1215/S0012-9074-02-11225-3</identifier><language>eng</language><publisher>DUKE University Press</publisher><subject>17B37 ; 20G42 ; 81R50 ; 82B23 ; Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20</subject><ispartof>Duke mathematical journal, 2002-04, Vol.112 (2), p.343-378</ispartof><rights>Copyright 2002 Duke University Press</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c346t-7ea4bee1c11bedbb05b1046a31e5ff750bf84412b4e03646b5e51d369bff92403</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,776,780,881,921,27901,27902</link.rule.ids></links><search><creatorcontrib>Nazarov, Maxim</creatorcontrib><creatorcontrib>Tarasov, Vitaly</creatorcontrib><title>On irreducibility of tensor products of Yangian modules associated with skew Young diagrams</title><title>Duke mathematical journal</title><description>We study the tensor product $W$ of any number of irreducible finite-dimensional modules $V\sb 1,\ldots V\sb k$ over the Yangian ${\rm Y}(\mathfrak {gl}\sb N)$ of the general linear Lie algebra $\mathfrak {gl}\sb N$. For any indices $i,j=1,\ldots k$, there is a canonical nonzero intertwining operator $J\sb {ij} : V\sb i\otimes V\sb j\to V\sb j\otimes V\sb i$. It has been conjectured that the tensor product $W$ is irreducible if and only if all operators $J\sb {ij}$ with $i<j$ are invertible. We prove this conjecture for a wide class of irreducible ${\rm Y}(\mathfrak {gl}\sb N)$-modules $V\sb 1,\ldots V\sb k$. Each of these modules is determined by a skew Young diagram and a complex parameter. We also introduce the notion of a Durfee rank of a skew Young diagram. For an ordinary Young diagram, this is the length of its main diagonal.</description><subject>17B37</subject><subject>20G42</subject><subject>81R50</subject><subject>82B23</subject><subject>Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20</subject><issn>0012-7094</issn><issn>1547-7398</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2002</creationdate><recordtype>article</recordtype><recordid>eNo9kNtKAzEQhoMoWKuPIOQFopkcNt07tagVCxVURL0Iye5sTQ-7Jdmivr3bA14N8zPfz_ARcg78AgToy2fOQbCcG8W4YABCaCYPSA-0MszIfHBIetsTw3N1TE5Smm3WPBM98jmpaYgRy3URfFiE9pc2FW2xTk2kq9h0eZs20burp8HVdNlFC0zUpdQUwbVY0u_QftE0x2_63qzrKS2Dm0a3TKfkqHKLhGf72Sevd7cvwxEbT-4fhtdjVkiVtcygUx4RCgCPpfdce-AqcxJQV5XR3FcDpUB4hVxmKvMaNZQyy31V5UJx2SdXu97u3xkWLa6LRSjtKoali7-2ccEOX8f7dD_K5cwCHxhtNGjdVehdRRGblCJW_zRwu5Fst5LtRrLlwm4lW9lxbMeF1OLPP-Ti3GZGGm1Npu3j3Y38eHobWZB_cESBKw</recordid><startdate>20020401</startdate><enddate>20020401</enddate><creator>Nazarov, Maxim</creator><creator>Tarasov, Vitaly</creator><general>DUKE University Press</general><general>Duke University Press</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20020401</creationdate><title>On irreducibility of tensor products of Yangian modules associated with skew Young diagrams</title><author>Nazarov, Maxim ; Tarasov, Vitaly</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c346t-7ea4bee1c11bedbb05b1046a31e5ff750bf84412b4e03646b5e51d369bff92403</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2002</creationdate><topic>17B37</topic><topic>20G42</topic><topic>81R50</topic><topic>82B23</topic><topic>Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nazarov, Maxim</creatorcontrib><creatorcontrib>Tarasov, Vitaly</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><jtitle>Duke mathematical journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nazarov, Maxim</au><au>Tarasov, Vitaly</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On irreducibility of tensor products of Yangian modules associated with skew Young diagrams</atitle><jtitle>Duke mathematical journal</jtitle><date>2002-04-01</date><risdate>2002</risdate><volume>112</volume><issue>2</issue><spage>343</spage><epage>378</epage><pages>343-378</pages><issn>0012-7094</issn><eissn>1547-7398</eissn><abstract>We study the tensor product $W$ of any number of irreducible finite-dimensional modules $V\sb 1,\ldots V\sb k$ over the Yangian ${\rm Y}(\mathfrak {gl}\sb N)$ of the general linear Lie algebra $\mathfrak {gl}\sb N$. For any indices $i,j=1,\ldots k$, there is a canonical nonzero intertwining operator $J\sb {ij} : V\sb i\otimes V\sb j\to V\sb j\otimes V\sb i$. It has been conjectured that the tensor product $W$ is irreducible if and only if all operators $J\sb {ij}$ with $i<j$ are invertible. We prove this conjecture for a wide class of irreducible ${\rm Y}(\mathfrak {gl}\sb N)$-modules $V\sb 1,\ldots V\sb k$. Each of these modules is determined by a skew Young diagram and a complex parameter. We also introduce the notion of a Durfee rank of a skew Young diagram. For an ordinary Young diagram, this is the length of its main diagonal.</abstract><pub>DUKE University Press</pub><doi>10.1215/S0012-9074-02-11225-3</doi><tpages>36</tpages></addata></record>
fulltext	fulltext
identifier	ISSN: 0012-7094
ispartof	Duke mathematical journal, 2002-04, Vol.112 (2), p.343-378
issn	0012-7094 1547-7398
language	eng
recordid	cdi_projecteuclid_primary_oai_CULeuclid_euclid_dmj_1087575155
source	Project Euclid Complete
subjects	17B37 20G42 81R50 82B23 Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20
title	On irreducibility of tensor products of Yangian modules associated with skew Young diagrams
url	https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-29T02%3A00%3A51IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-istex_proje&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20irreducibility%20of%20tensor%20products%20of%20Yangian%20modules%20associated%20with%20skew%20Young%20diagrams&rft.jtitle=Duke%20mathematical%20journal&rft.au=Nazarov,%20Maxim&rft.date=2002-04-01&rft.volume=112&rft.issue=2&rft.spage=343&rft.epage=378&rft.pages=343-378&rft.issn=0012-7094&rft.eissn=1547-7398&rft_id=info:doi/10.1215/S0012-9074-02-11225-3&rft_dat=%3Cistex_proje%3Eark_67375_765_KFB3ZPWH_1%3C/istex_proje%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