{"title":"超Schrödinger代数的准whittaker超模","authors":"Xinyue Wang , Liangyun Chen , Yao Ma","doi":"10.1016/j.geomphys.2025.105490","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, let <span><math><mi>S</mi></math></span> denote the <span><math><mi>N</mi><mo>=</mo><mn>1</mn></math></span> super Schrödinger algebra in <span><math><mo>(</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-dimensional spacetime. We first define the (universal) quasi-Whittaker supermodules and quasi-Whittaker vectors over <span><math><mi>S</mi></math></span>. Then we prove that any simple <span><math><mi>S</mi></math></span>-supermodule is a quasi-Whittaker supermodule if and only if it is a locally finite supermodule over the Heisenberg subalgebra of <span><math><mi>S</mi></math></span>. We also describe all quasi-Whittaker vectors of the universal quasi-Whittaker supermodule and its quotient module. At last, we give the classification of simple quasi-Whittaker <span><math><mi>S</mi></math></span>-supermodules.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"213 ","pages":"Article 105490"},"PeriodicalIF":1.2000,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quasi-Whittaker supermodules for the super Schrödinger algebra\",\"authors\":\"Xinyue Wang , Liangyun Chen , Yao Ma\",\"doi\":\"10.1016/j.geomphys.2025.105490\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, let <span><math><mi>S</mi></math></span> denote the <span><math><mi>N</mi><mo>=</mo><mn>1</mn></math></span> super Schrödinger algebra in <span><math><mo>(</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-dimensional spacetime. We first define the (universal) quasi-Whittaker supermodules and quasi-Whittaker vectors over <span><math><mi>S</mi></math></span>. Then we prove that any simple <span><math><mi>S</mi></math></span>-supermodule is a quasi-Whittaker supermodule if and only if it is a locally finite supermodule over the Heisenberg subalgebra of <span><math><mi>S</mi></math></span>. We also describe all quasi-Whittaker vectors of the universal quasi-Whittaker supermodule and its quotient module. At last, we give the classification of simple quasi-Whittaker <span><math><mi>S</mi></math></span>-supermodules.</div></div>\",\"PeriodicalId\":55602,\"journal\":{\"name\":\"Journal of Geometry and Physics\",\"volume\":\"213 \",\"pages\":\"Article 105490\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2025-03-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Geometry and Physics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0393044025000749\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Geometry and Physics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0393044025000749","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Quasi-Whittaker supermodules for the super Schrödinger algebra
In this paper, let denote the super Schrödinger algebra in -dimensional spacetime. We first define the (universal) quasi-Whittaker supermodules and quasi-Whittaker vectors over . Then we prove that any simple -supermodule is a quasi-Whittaker supermodule if and only if it is a locally finite supermodule over the Heisenberg subalgebra of . We also describe all quasi-Whittaker vectors of the universal quasi-Whittaker supermodule and its quotient module. At last, we give the classification of simple quasi-Whittaker -supermodules.
期刊介绍:
The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields.
The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered.
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