{"title":"E 型量子仿射代数的第 1 级不可还原最高权重和 Fock 空间晶体的杨墙变现","authors":"Duncan Laurie","doi":"10.1016/j.jalgebra.2024.07.047","DOIUrl":null,"url":null,"abstract":"<div><p>We construct Young wall models for the crystal bases of level 1 irreducible highest weight representations and Fock space representations of quantum affine algebras in types <span><math><msubsup><mrow><mi>E</mi></mrow><mrow><mn>6</mn></mrow><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup></math></span>, <span><math><msubsup><mrow><mi>E</mi></mrow><mrow><mn>7</mn></mrow><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup></math></span> and <span><math><msubsup><mrow><mi>E</mi></mrow><mrow><mn>8</mn></mrow><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup></math></span>. In each case, Young walls consist of coloured blocks stacked inside the relevant Young wall pattern which satisfy a certain combinatorial condition. Moreover the crystal structure is described entirely in terms of adding and removing blocks.</p></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0021869324004435/pdfft?md5=6b79cb729bc707ce4fc305a109a070ec&pid=1-s2.0-S0021869324004435-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Young wall realizations of level 1 irreducible highest weight and Fock space crystals of quantum affine algebras in type E\",\"authors\":\"Duncan Laurie\",\"doi\":\"10.1016/j.jalgebra.2024.07.047\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We construct Young wall models for the crystal bases of level 1 irreducible highest weight representations and Fock space representations of quantum affine algebras in types <span><math><msubsup><mrow><mi>E</mi></mrow><mrow><mn>6</mn></mrow><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup></math></span>, <span><math><msubsup><mrow><mi>E</mi></mrow><mrow><mn>7</mn></mrow><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup></math></span> and <span><math><msubsup><mrow><mi>E</mi></mrow><mrow><mn>8</mn></mrow><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msubsup></math></span>. In each case, Young walls consist of coloured blocks stacked inside the relevant Young wall pattern which satisfy a certain combinatorial condition. Moreover the crystal structure is described entirely in terms of adding and removing blocks.</p></div>\",\"PeriodicalId\":14888,\"journal\":{\"name\":\"Journal of Algebra\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-08-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0021869324004435/pdfft?md5=6b79cb729bc707ce4fc305a109a070ec&pid=1-s2.0-S0021869324004435-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021869324004435\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021869324004435","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Young wall realizations of level 1 irreducible highest weight and Fock space crystals of quantum affine algebras in type E
We construct Young wall models for the crystal bases of level 1 irreducible highest weight representations and Fock space representations of quantum affine algebras in types , and . In each case, Young walls consist of coloured blocks stacked inside the relevant Young wall pattern which satisfy a certain combinatorial condition. Moreover the crystal structure is described entirely in terms of adding and removing blocks.
期刊介绍:
The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.