Newton strata in Levi subgroups
Certain Iwahori double cosets in the loop group of a reductive group, known under the names of P -alcoves or ( J , w , δ ) -alcoves, play an important role in the study of affine Deligne–Lusztig varieties. For such an Iwahori double coset, its Newton stratification is related to the Newton stratific...
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| Veröffentlicht in: | Manuscripta mathematica 2024-09, Vol.175 (1-2), p.513-519 |
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| creator | Schremmer, Felix |
| description | Certain Iwahori double cosets in the loop group of a reductive group, known under the names of
P
-alcoves or
(
J
,
w
,
δ
)
-alcoves, play an important role in the study of affine Deligne–Lusztig varieties. For such an Iwahori double coset, its Newton stratification is related to the Newton stratification of an Iwahori double coset in a Levi subgroup. We study this relationship further, providing in particular a bijection between the occurring Newton strata. As an application, we prove a conjecture of Dong-Gyu Lim, giving a non-emptiness criterion for basic affine Deligne–Lusztig varieties. |
| doi_str_mv | 10.1007/s00229-024-01566-y |
| format | Article |
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P
-alcoves or
(
J
,
w
,
δ
)
-alcoves, play an important role in the study of affine Deligne–Lusztig varieties. For such an Iwahori double coset, its Newton stratification is related to the Newton stratification of an Iwahori double coset in a Levi subgroup. We study this relationship further, providing in particular a bijection between the occurring Newton strata. As an application, we prove a conjecture of Dong-Gyu Lim, giving a non-emptiness criterion for basic affine Deligne–Lusztig varieties.</description><identifier>ISSN: 0025-2611</identifier><identifier>EISSN: 1432-1785</identifier><identifier>DOI: 10.1007/s00229-024-01566-y</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Algebraic Geometry ; Calculus of Variations and Optimal Control; Optimization ; Geometry ; Lie Groups ; Mathematics ; Mathematics and Statistics ; Number Theory ; Stratification ; Subgroups ; Topological Groups</subject><ispartof>Manuscripta mathematica, 2024-09, Vol.175 (1-2), p.513-519</ispartof><rights>The Author(s) 2024</rights><rights>The Author(s) 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c244t-96e1c53830f6f9d0143dcf9db953cba98acd01bba618f6aca46ff825b6142c663</cites><orcidid>0000-0002-3894-3894</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00229-024-01566-y$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00229-024-01566-y$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Schremmer, Felix</creatorcontrib><title>Newton strata in Levi subgroups</title><title>Manuscripta mathematica</title><addtitle>manuscripta math</addtitle><description>Certain Iwahori double cosets in the loop group of a reductive group, known under the names of
P
-alcoves or
(
J
,
w
,
δ
)
-alcoves, play an important role in the study of affine Deligne–Lusztig varieties. For such an Iwahori double coset, its Newton stratification is related to the Newton stratification of an Iwahori double coset in a Levi subgroup. We study this relationship further, providing in particular a bijection between the occurring Newton strata. As an application, we prove a conjecture of Dong-Gyu Lim, giving a non-emptiness criterion for basic affine Deligne–Lusztig varieties.</description><subject>Algebraic Geometry</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Geometry</subject><subject>Lie Groups</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Number Theory</subject><subject>Stratification</subject><subject>Subgroups</subject><subject>Topological Groups</subject><issn>0025-2611</issn><issn>1432-1785</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9kE1LxDAQhoMoWFf_gBcLnqP5nDZHWfyCohc9hySbLF20rUmr9N-btYI3TzPMvO87zIPQOSVXlJDqOhHCmMKECUyoBMDzASqo4AzTqpaHqMh7iRlQeoxOUtoRkpcVL9DFk_8a-65MYzSjKduubPxnW6bJbmM_DekUHQXzlvzZb12h17vbl_UDbp7vH9c3DXZMiBEr8NRJXnMSIKjNPn3jcmOV5M4aVRuXh9YaoHUA44yAEGomLVDBHABfocsld4j9x-TTqHf9FLt8UnOiACB_ybOKLSoX-5SiD3qI7buJs6ZE70HoBYTOIPQPCD1nE19MKYu7rY9_0f-4vgGLd1_Z</recordid><startdate>20240901</startdate><enddate>20240901</enddate><creator>Schremmer, Felix</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-3894-3894</orcidid></search><sort><creationdate>20240901</creationdate><title>Newton strata in Levi subgroups</title><author>Schremmer, Felix</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c244t-96e1c53830f6f9d0143dcf9db953cba98acd01bba618f6aca46ff825b6142c663</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Algebraic Geometry</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Geometry</topic><topic>Lie Groups</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Number Theory</topic><topic>Stratification</topic><topic>Subgroups</topic><topic>Topological Groups</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Schremmer, Felix</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><jtitle>Manuscripta mathematica</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Schremmer, Felix</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Newton strata in Levi subgroups</atitle><jtitle>Manuscripta mathematica</jtitle><stitle>manuscripta math</stitle><date>2024-09-01</date><risdate>2024</risdate><volume>175</volume><issue>1-2</issue><spage>513</spage><epage>519</epage><pages>513-519</pages><issn>0025-2611</issn><eissn>1432-1785</eissn><abstract>Certain Iwahori double cosets in the loop group of a reductive group, known under the names of
P
-alcoves or
(
J
,
w
,
δ
)
-alcoves, play an important role in the study of affine Deligne–Lusztig varieties. For such an Iwahori double coset, its Newton stratification is related to the Newton stratification of an Iwahori double coset in a Levi subgroup. We study this relationship further, providing in particular a bijection between the occurring Newton strata. As an application, we prove a conjecture of Dong-Gyu Lim, giving a non-emptiness criterion for basic affine Deligne–Lusztig varieties.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00229-024-01566-y</doi><tpages>7</tpages><orcidid>https://orcid.org/0000-0002-3894-3894</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0025-2611 |
| ispartof | Manuscripta mathematica, 2024-09, Vol.175 (1-2), p.513-519 |
| issn | 0025-2611 1432-1785 |
| language | eng |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Algebraic Geometry Calculus of Variations and Optimal Control Optimization Geometry Lie Groups Mathematics Mathematics and Statistics Number Theory Stratification Subgroups Topological Groups |
| title | Newton strata in Levi subgroups |
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