{"title":"关于幂偶群的Howe结果的推广","authors":"Souha Maaref","doi":"10.1016/j.bulsci.2024.103536","DOIUrl":null,"url":null,"abstract":"<div><div>Let <em>F</em> be a nonarchimedean local field of characteristic zero and <strong>G</strong> be a unipotent algebraic group defined over <em>F</em>. The set of rational points of <strong>G</strong>, denoted by <em>G</em>, is a <em>p</em>-adic Lie group. Let <span><math><mi>g</mi></math></span> be the Lie algebra of <em>G</em>. Now let <em>H</em> be a normal closed subgroup of <em>G</em>, <em>χ</em> be a unitary character of <em>H</em> and <em>π</em> be an irreducible unitary representation of <em>G</em> in a Hilbert space <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>π</mi></mrow></msub></math></span>. The aim of this paper is the determination of the space formed by the <em>χ</em>-semi-invariant vectors of <em>π</em>.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"198 ","pages":"Article 103536"},"PeriodicalIF":0.9000,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On a generalization of a result of Howe for unipotent groups\",\"authors\":\"Souha Maaref\",\"doi\":\"10.1016/j.bulsci.2024.103536\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Let <em>F</em> be a nonarchimedean local field of characteristic zero and <strong>G</strong> be a unipotent algebraic group defined over <em>F</em>. The set of rational points of <strong>G</strong>, denoted by <em>G</em>, is a <em>p</em>-adic Lie group. Let <span><math><mi>g</mi></math></span> be the Lie algebra of <em>G</em>. Now let <em>H</em> be a normal closed subgroup of <em>G</em>, <em>χ</em> be a unitary character of <em>H</em> and <em>π</em> be an irreducible unitary representation of <em>G</em> in a Hilbert space <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>π</mi></mrow></msub></math></span>. The aim of this paper is the determination of the space formed by the <em>χ</em>-semi-invariant vectors of <em>π</em>.</div></div>\",\"PeriodicalId\":55313,\"journal\":{\"name\":\"Bulletin des Sciences Mathematiques\",\"volume\":\"198 \",\"pages\":\"Article 103536\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-11-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin des Sciences Mathematiques\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0007449724001544\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin des Sciences Mathematiques","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0007449724001544","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
On a generalization of a result of Howe for unipotent groups
Let F be a nonarchimedean local field of characteristic zero and G be a unipotent algebraic group defined over F. The set of rational points of G, denoted by G, is a p-adic Lie group. Let be the Lie algebra of G. Now let H be a normal closed subgroup of G, χ be a unitary character of H and π be an irreducible unitary representation of G in a Hilbert space . The aim of this paper is the determination of the space formed by the χ-semi-invariant vectors of π.