ON EXTENDED WEIGHT MONOIDS OF SPHERICAL HOMOGENEOUS SPACES
Given a connected reductive complex algebraic group G and a spherical subgroup H ⊂ G , the extended weight monoid Λ ̂ G + G / H encodes the G -module structures on spaces of global sections of all G -linearized line bundles on G / H . Assuming that G is semisimple and simply connected and H is speci...
Gespeichert in:
| Veröffentlicht in: | Transformation groups 2021-06, Vol.26 (2), p.403-431 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 431 |
|---|---|
| container_issue | 2 |
| container_start_page | 403 |
| container_title | Transformation groups |
| container_volume | 26 |
| creator | AVDEEV, ROMAN |
| description | Given a connected reductive complex algebraic group
G
and a spherical subgroup
H
⊂
G
, the extended weight monoid
Λ
̂
G
+
G
/
H
encodes the
G
-module structures on spaces of global sections of all
G
-linearized line bundles on
G
/
H
. Assuming that
G
is semisimple and simply connected and
H
is specified by a regular embedding in a parabolic subgroup
P
⊂
G
, in this paper we obtain a description of
Λ
̂
G
+
G
/
H
via the set of simple spherical roots of
G
/
H
together with certain combinatorial data explicitly computed from the pair (
P
;
H
). As an application, we deduce a new proof of a result of Avdeev and Gorfinkel describing
Λ
̂
G
+
G
/
H
in the case where
H
is strongly solvable. |
| doi_str_mv | 10.1007/s00031-021-09642-3 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2549709009</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2549709009</sourcerecordid><originalsourceid>FETCH-LOGICAL-c319t-ce54af4e172cb67d6382f3e96b97cce44cec3e4f471f769141d31007fde16b5e3</originalsourceid><addsrcrecordid>eNp9kE9PAjEQxRujiYh-AU-beF6d_tmWeiNQ2E1ga1yI3BoorZEoYAsHv73FNfHmYTKTyfu9yTyEbjHcYwDxEAGA4hxIKskZyekZ6uAirYoeX5ynGXo0Z5STS3QV4wYAC855Bz3qOlOLmaqHapi9qGpczrKprnU1bDI9ypqnUj1Xg_4kK_VUj1Wt9LxJ2_5ANdfowi_fo7v57V00H6nZoMwnenxCckuxPOTWFWzpmcOC2BUXa057xFMn-UoKax1j1lnqmGcCe8ElZnhNTz_5tcN8VTjaRXet7z7sPo8uHsxmdwzbdNKQgkkBEkAmFWlVNuxiDM6bfXj7WIYvg8Gc_EybkUkZmZ-MDE0QbaGYxNtXF_6s_6G-Abu6Yy4</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2549709009</pqid></control><display><type>article</type><title>ON EXTENDED WEIGHT MONOIDS OF SPHERICAL HOMOGENEOUS SPACES</title><source>SpringerLink_现刊</source><creator>AVDEEV, ROMAN</creator><creatorcontrib>AVDEEV, ROMAN</creatorcontrib><description>Given a connected reductive complex algebraic group
G
and a spherical subgroup
H
⊂
G
, the extended weight monoid
Λ
̂
G
+
G
/
H
encodes the
G
-module structures on spaces of global sections of all
G
-linearized line bundles on
G
/
H
. Assuming that
G
is semisimple and simply connected and
H
is specified by a regular embedding in a parabolic subgroup
P
⊂
G
, in this paper we obtain a description of
Λ
̂
G
+
G
/
H
via the set of simple spherical roots of
G
/
H
together with certain combinatorial data explicitly computed from the pair (
P
;
H
). As an application, we deduce a new proof of a result of Avdeev and Gorfinkel describing
Λ
̂
G
+
G
/
H
in the case where
H
is strongly solvable.</description><identifier>ISSN: 1083-4362</identifier><identifier>EISSN: 1531-586X</identifier><identifier>DOI: 10.1007/s00031-021-09642-3</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algebra ; Combinatorial analysis ; Lie Groups ; Mathematics ; Mathematics and Statistics ; Monoids ; Subgroups ; Topological Groups ; Weight</subject><ispartof>Transformation groups, 2021-06, Vol.26 (2), p.403-431</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021</rights><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-ce54af4e172cb67d6382f3e96b97cce44cec3e4f471f769141d31007fde16b5e3</citedby><cites>FETCH-LOGICAL-c319t-ce54af4e172cb67d6382f3e96b97cce44cec3e4f471f769141d31007fde16b5e3</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/s00031-021-09642-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00031-021-09642-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>AVDEEV, ROMAN</creatorcontrib><title>ON EXTENDED WEIGHT MONOIDS OF SPHERICAL HOMOGENEOUS SPACES</title><title>Transformation groups</title><addtitle>Transformation Groups</addtitle><description>Given a connected reductive complex algebraic group
G
and a spherical subgroup
H
⊂
G
, the extended weight monoid
Λ
̂
G
+
G
/
H
encodes the
G
-module structures on spaces of global sections of all
G
-linearized line bundles on
G
/
H
. Assuming that
G
is semisimple and simply connected and
H
is specified by a regular embedding in a parabolic subgroup
P
⊂
G
, in this paper we obtain a description of
Λ
̂
G
+
G
/
H
via the set of simple spherical roots of
G
/
H
together with certain combinatorial data explicitly computed from the pair (
P
;
H
). As an application, we deduce a new proof of a result of Avdeev and Gorfinkel describing
Λ
̂
G
+
G
/
H
in the case where
H
is strongly solvable.</description><subject>Algebra</subject><subject>Combinatorial analysis</subject><subject>Lie Groups</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Monoids</subject><subject>Subgroups</subject><subject>Topological Groups</subject><subject>Weight</subject><issn>1083-4362</issn><issn>1531-586X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kE9PAjEQxRujiYh-AU-beF6d_tmWeiNQ2E1ga1yI3BoorZEoYAsHv73FNfHmYTKTyfu9yTyEbjHcYwDxEAGA4hxIKskZyekZ6uAirYoeX5ynGXo0Z5STS3QV4wYAC855Bz3qOlOLmaqHapi9qGpczrKprnU1bDI9ypqnUj1Xg_4kK_VUj1Wt9LxJ2_5ANdfowi_fo7v57V00H6nZoMwnenxCckuxPOTWFWzpmcOC2BUXa057xFMn-UoKax1j1lnqmGcCe8ElZnhNTz_5tcN8VTjaRXet7z7sPo8uHsxmdwzbdNKQgkkBEkAmFWlVNuxiDM6bfXj7WIYvg8Gc_EybkUkZmZ-MDE0QbaGYxNtXF_6s_6G-Abu6Yy4</recordid><startdate>20210601</startdate><enddate>20210601</enddate><creator>AVDEEV, ROMAN</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20210601</creationdate><title>ON EXTENDED WEIGHT MONOIDS OF SPHERICAL HOMOGENEOUS SPACES</title><author>AVDEEV, ROMAN</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-ce54af4e172cb67d6382f3e96b97cce44cec3e4f471f769141d31007fde16b5e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Algebra</topic><topic>Combinatorial analysis</topic><topic>Lie Groups</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Monoids</topic><topic>Subgroups</topic><topic>Topological Groups</topic><topic>Weight</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>AVDEEV, ROMAN</creatorcontrib><collection>CrossRef</collection><jtitle>Transformation groups</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>AVDEEV, ROMAN</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>ON EXTENDED WEIGHT MONOIDS OF SPHERICAL HOMOGENEOUS SPACES</atitle><jtitle>Transformation groups</jtitle><stitle>Transformation Groups</stitle><date>2021-06-01</date><risdate>2021</risdate><volume>26</volume><issue>2</issue><spage>403</spage><epage>431</epage><pages>403-431</pages><issn>1083-4362</issn><eissn>1531-586X</eissn><abstract>Given a connected reductive complex algebraic group
G
and a spherical subgroup
H
⊂
G
, the extended weight monoid
Λ
̂
G
+
G
/
H
encodes the
G
-module structures on spaces of global sections of all
G
-linearized line bundles on
G
/
H
. Assuming that
G
is semisimple and simply connected and
H
is specified by a regular embedding in a parabolic subgroup
P
⊂
G
, in this paper we obtain a description of
Λ
̂
G
+
G
/
H
via the set of simple spherical roots of
G
/
H
together with certain combinatorial data explicitly computed from the pair (
P
;
H
). As an application, we deduce a new proof of a result of Avdeev and Gorfinkel describing
Λ
̂
G
+
G
/
H
in the case where
H
is strongly solvable.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00031-021-09642-3</doi><tpages>29</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1083-4362 |
| ispartof | Transformation groups, 2021-06, Vol.26 (2), p.403-431 |
| issn | 1083-4362 1531-586X |
| language | eng |
| recordid | cdi_proquest_journals_2549709009 |
| source | SpringerLink_现刊 |
| subjects | Algebra Combinatorial analysis Lie Groups Mathematics Mathematics and Statistics Monoids Subgroups Topological Groups Weight |
| title | ON EXTENDED WEIGHT MONOIDS OF SPHERICAL HOMOGENEOUS SPACES |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-20T13%3A34%3A04IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=ON%20EXTENDED%20WEIGHT%20MONOIDS%20OF%20SPHERICAL%20HOMOGENEOUS%20SPACES&rft.jtitle=Transformation%20groups&rft.au=AVDEEV,%20ROMAN&rft.date=2021-06-01&rft.volume=26&rft.issue=2&rft.spage=403&rft.epage=431&rft.pages=403-431&rft.issn=1083-4362&rft.eissn=1531-586X&rft_id=info:doi/10.1007/s00031-021-09642-3&rft_dat=%3Cproquest_cross%3E2549709009%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2549709009&rft_id=info:pmid/&rfr_iscdi=true |