THE COMPONENTS OF THE SINGULAR LOCUS OF A COMPONENT OF A SPRINGER FIBER OVER x2 = 0
For x ∈ End(K n ) satisfying x 2 = 0 let F x be the variety of full flags stable under the action of x (Springer fiber over x ). The full classification of the components of F x according to their smoothness was provided in [4] in terms of both Young tableaux and link patterns. Moreover in [2] the p...
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| Veröffentlicht in: | Transformation groups 2022, Vol.27 (2), p.597-633 |
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| creator | MANSOUR, RONIT MELNIKOV, ANNA |
| description | For
x
∈ End(K
n
) satisfying
x
2
= 0 let F
x
be the variety of full flags stable under the action of
x
(Springer fiber over
x
). The full classification of the components of F
x
according to their smoothness was provided in [4] in terms of both Young tableaux and link patterns. Moreover in [2] the purely combinatorial algorithm to compute the singular locus of a singular component of F
x
is provided. However, this algorithm involves the computation of the graph of the component, and the complexity of computations grows very quickly, so that in practice it is impossible to use it. In this paper, we construct another algorithm, giving all the components of the singular locus of a singular component F
σ
of F
x
in terms of link patterns constructed straightforwardly from the link pattern of σ. |
| doi_str_mv | 10.1007/s00031-020-09621-0 |
| format | Article |
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x
∈ End(K
n
) satisfying
x
2
= 0 let F
x
be the variety of full flags stable under the action of
x
(Springer fiber over
x
). The full classification of the components of F
x
according to their smoothness was provided in [4] in terms of both Young tableaux and link patterns. Moreover in [2] the purely combinatorial algorithm to compute the singular locus of a singular component of F
x
is provided. However, this algorithm involves the computation of the graph of the component, and the complexity of computations grows very quickly, so that in practice it is impossible to use it. In this paper, we construct another algorithm, giving all the components of the singular locus of a singular component F
σ
of F
x
in terms of link patterns constructed straightforwardly from the link pattern of σ.</description><identifier>ISSN: 1083-4362</identifier><identifier>EISSN: 1531-586X</identifier><identifier>DOI: 10.1007/s00031-020-09621-0</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algebra ; Algorithms ; Combinatorial analysis ; Lie Groups ; Loci ; Mathematics ; Mathematics and Statistics ; Smoothness ; Topological Groups</subject><ispartof>Transformation groups, 2022, Vol.27 (2), p.597-633</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2020</rights><rights>Springer Science+Business Media, LLC, part of Springer Nature 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c1640-5e9ec385eeb18cc7756e01d72fc68a370433559b49dda4ecf5353c9679fc73683</citedby><cites>FETCH-LOGICAL-c1640-5e9ec385eeb18cc7756e01d72fc68a370433559b49dda4ecf5353c9679fc73683</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/s00031-020-09621-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00031-020-09621-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>MANSOUR, RONIT</creatorcontrib><creatorcontrib>MELNIKOV, ANNA</creatorcontrib><title>THE COMPONENTS OF THE SINGULAR LOCUS OF A COMPONENT OF A SPRINGER FIBER OVER x2 = 0</title><title>Transformation groups</title><addtitle>Transformation Groups</addtitle><description>For
x
∈ End(K
n
) satisfying
x
2
= 0 let F
x
be the variety of full flags stable under the action of
x
(Springer fiber over
x
). The full classification of the components of F
x
according to their smoothness was provided in [4] in terms of both Young tableaux and link patterns. Moreover in [2] the purely combinatorial algorithm to compute the singular locus of a singular component of F
x
is provided. However, this algorithm involves the computation of the graph of the component, and the complexity of computations grows very quickly, so that in practice it is impossible to use it. In this paper, we construct another algorithm, giving all the components of the singular locus of a singular component F
σ
of F
x
in terms of link patterns constructed straightforwardly from the link pattern of σ.</description><subject>Algebra</subject><subject>Algorithms</subject><subject>Combinatorial analysis</subject><subject>Lie Groups</subject><subject>Loci</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Smoothness</subject><subject>Topological Groups</subject><issn>1083-4362</issn><issn>1531-586X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kF1LwzAUhoMoOKd_wKuA19WTpEmaCy9q6T6grmPdxLvQpak4dJvJBvrvzVZhd96cj5fnPQdehG4J3BMA-eABgJEIKESgBA3TGeoRHiSeiNfzMEPCopgJeomuvF8BECmE6KFqPspxVj5Py0k-mVe4HOCDUo0nw0WRznBRZoujmp6obq2mswDlMzwYP4VavoTyTfEjhmt00dYf3t789T5aDPJ5NoqKcjjO0iIyRMQQcausYQm3dkkSY6TkwgJpJG2NSGomIWaMc7WMVdPUsTUtZ5wZJaRqjWQiYX10193dus3X3vqdXm32bh1eaiokYaCIigNFO8q4jffOtnrr3j9r96MJ6EN4ugtPh_D0MTwNwcQ6kw_w-s260-l_XL8IhGha</recordid><startdate>2022</startdate><enddate>2022</enddate><creator>MANSOUR, RONIT</creator><creator>MELNIKOV, ANNA</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>2022</creationdate><title>THE COMPONENTS OF THE SINGULAR LOCUS OF A COMPONENT OF A SPRINGER FIBER OVER x2 = 0</title><author>MANSOUR, RONIT ; MELNIKOV, ANNA</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c1640-5e9ec385eeb18cc7756e01d72fc68a370433559b49dda4ecf5353c9679fc73683</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Algebra</topic><topic>Algorithms</topic><topic>Combinatorial analysis</topic><topic>Lie Groups</topic><topic>Loci</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Smoothness</topic><topic>Topological Groups</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>MANSOUR, RONIT</creatorcontrib><creatorcontrib>MELNIKOV, ANNA</creatorcontrib><collection>CrossRef</collection><jtitle>Transformation groups</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>MANSOUR, RONIT</au><au>MELNIKOV, ANNA</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>THE COMPONENTS OF THE SINGULAR LOCUS OF A COMPONENT OF A SPRINGER FIBER OVER x2 = 0</atitle><jtitle>Transformation groups</jtitle><stitle>Transformation Groups</stitle><date>2022</date><risdate>2022</risdate><volume>27</volume><issue>2</issue><spage>597</spage><epage>633</epage><pages>597-633</pages><issn>1083-4362</issn><eissn>1531-586X</eissn><abstract>For
x
∈ End(K
n
) satisfying
x
2
= 0 let F
x
be the variety of full flags stable under the action of
x
(Springer fiber over
x
). The full classification of the components of F
x
according to their smoothness was provided in [4] in terms of both Young tableaux and link patterns. Moreover in [2] the purely combinatorial algorithm to compute the singular locus of a singular component of F
x
is provided. However, this algorithm involves the computation of the graph of the component, and the complexity of computations grows very quickly, so that in practice it is impossible to use it. In this paper, we construct another algorithm, giving all the components of the singular locus of a singular component F
σ
of F
x
in terms of link patterns constructed straightforwardly from the link pattern of σ.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00031-020-09621-0</doi><tpages>37</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1083-4362 |
| ispartof | Transformation groups, 2022, Vol.27 (2), p.597-633 |
| issn | 1083-4362 1531-586X |
| language | eng |
| recordid | cdi_proquest_journals_2671309194 |
| source | SpringerLink Journals |
| subjects | Algebra Algorithms Combinatorial analysis Lie Groups Loci Mathematics Mathematics and Statistics Smoothness Topological Groups |
| title | THE COMPONENTS OF THE SINGULAR LOCUS OF A COMPONENT OF A SPRINGER FIBER OVER x2 = 0 |
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