{"title":"还原群作用的交映复杂性","authors":"Avraham Aizenbud, Dmitry Gourevitch","doi":"10.1016/j.indag.2024.03.010","DOIUrl":null,"url":null,"abstract":"<div><div>Let a complex algebraic reductive group <span><math><mi>G</mi></math></span> act on a complex algebraic manifold <span><math><mi>X</mi></math></span>. For a <span><math><mi>G</mi></math></span>-invariant subvariety <span><math><mi>Ξ</mi></math></span> of the nilpotent cone <span><math><mrow><mi>N</mi><mrow><mo>(</mo><msup><mrow><mi>g</mi></mrow><mrow><mo>∗</mo></mrow></msup><mo>)</mo></mrow><mo>⊂</mo><msup><mrow><mi>g</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span> we define a notion of <span><math><mi>Ξ</mi></math></span>-symplectic complexity of <span><math><mi>X</mi></math></span>. This notion generalizes the notion of complexity defined in Vinberg (1986). We prove several properties of this notion, and relate it to the notion of <span><math><mi>Ξ</mi></math></span>-complexity defined in Aizenbud and Gourevitch (2024) motivated by its relation with representation theory.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"36 2","pages":"Pages 703-712"},"PeriodicalIF":0.5000,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Symplectic complexity of reductive group actions\",\"authors\":\"Avraham Aizenbud, Dmitry Gourevitch\",\"doi\":\"10.1016/j.indag.2024.03.010\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Let a complex algebraic reductive group <span><math><mi>G</mi></math></span> act on a complex algebraic manifold <span><math><mi>X</mi></math></span>. For a <span><math><mi>G</mi></math></span>-invariant subvariety <span><math><mi>Ξ</mi></math></span> of the nilpotent cone <span><math><mrow><mi>N</mi><mrow><mo>(</mo><msup><mrow><mi>g</mi></mrow><mrow><mo>∗</mo></mrow></msup><mo>)</mo></mrow><mo>⊂</mo><msup><mrow><mi>g</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span> we define a notion of <span><math><mi>Ξ</mi></math></span>-symplectic complexity of <span><math><mi>X</mi></math></span>. This notion generalizes the notion of complexity defined in Vinberg (1986). We prove several properties of this notion, and relate it to the notion of <span><math><mi>Ξ</mi></math></span>-complexity defined in Aizenbud and Gourevitch (2024) motivated by its relation with representation theory.</div></div>\",\"PeriodicalId\":56126,\"journal\":{\"name\":\"Indagationes Mathematicae-New Series\",\"volume\":\"36 2\",\"pages\":\"Pages 703-712\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-03-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indagationes Mathematicae-New Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0019357724000193\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae-New Series","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0019357724000193","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Let a complex algebraic reductive group act on a complex algebraic manifold . For a -invariant subvariety of the nilpotent cone we define a notion of -symplectic complexity of . This notion generalizes the notion of complexity defined in Vinberg (1986). We prove several properties of this notion, and relate it to the notion of -complexity defined in Aizenbud and Gourevitch (2024) motivated by its relation with representation theory.
期刊介绍:
Indagationes Mathematicae is a peer-reviewed international journal for the Mathematical Sciences of the Royal Dutch Mathematical Society. The journal aims at the publication of original mathematical research papers of high quality and of interest to a large segment of the mathematics community. The journal also welcomes the submission of review papers of high quality.