{"title":"量子仿正交超代数的振子表示","authors":"Jae-Hoon Kwon, Sin-Myung Lee, Masato Okado","doi":"10.1007/s00220-024-04961-4","DOIUrl":null,"url":null,"abstract":"<p>We introduce a category of <i>q</i>-oscillator representations over the quantum affine superalgebras of type <i>D</i> and construct a new family of its irreducible representations. Motivated by the theory of super duality, we show that these irreducible representations naturally interpolate the irreducible <i>q</i>-oscillator representations of type <span>\\(X_n^{(1)}\\)</span> and the finite-dimensional irreducible representations of type <span>\\(Y_n^{(1)}\\)</span> for <span>\\((X,Y)=(C,D),(D,C)\\)</span> under exact monoidal functors. This can be viewed as a quantum (untwisted) affine analogue of the correspondence between irreducible oscillator and irreducible finite-dimensional representations of classical Lie algebras arising from Howe’s reductive dual pairs <span>\\((\\mathfrak {g},G)\\)</span>, where <span>\\(\\mathfrak {g}=\\mathfrak {sp}_{2n}, \\mathfrak {so}_{2n}\\)</span> and <span>\\(G=O_\\ell , Sp_{2\\ell }\\)</span>.</p>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Oscillator Representations of Quantum Affine Orthosymplectic Superalgebras\",\"authors\":\"Jae-Hoon Kwon, Sin-Myung Lee, Masato Okado\",\"doi\":\"10.1007/s00220-024-04961-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We introduce a category of <i>q</i>-oscillator representations over the quantum affine superalgebras of type <i>D</i> and construct a new family of its irreducible representations. Motivated by the theory of super duality, we show that these irreducible representations naturally interpolate the irreducible <i>q</i>-oscillator representations of type <span>\\\\(X_n^{(1)}\\\\)</span> and the finite-dimensional irreducible representations of type <span>\\\\(Y_n^{(1)}\\\\)</span> for <span>\\\\((X,Y)=(C,D),(D,C)\\\\)</span> under exact monoidal functors. This can be viewed as a quantum (untwisted) affine analogue of the correspondence between irreducible oscillator and irreducible finite-dimensional representations of classical Lie algebras arising from Howe’s reductive dual pairs <span>\\\\((\\\\mathfrak {g},G)\\\\)</span>, where <span>\\\\(\\\\mathfrak {g}=\\\\mathfrak {sp}_{2n}, \\\\mathfrak {so}_{2n}\\\\)</span> and <span>\\\\(G=O_\\\\ell , Sp_{2\\\\ell }\\\\)</span>.</p>\",\"PeriodicalId\":522,\"journal\":{\"name\":\"Communications in Mathematical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-04-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1007/s00220-024-04961-4\",\"RegionNum\":1,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s00220-024-04961-4","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
Oscillator Representations of Quantum Affine Orthosymplectic Superalgebras
We introduce a category of q-oscillator representations over the quantum affine superalgebras of type D and construct a new family of its irreducible representations. Motivated by the theory of super duality, we show that these irreducible representations naturally interpolate the irreducible q-oscillator representations of type \(X_n^{(1)}\) and the finite-dimensional irreducible representations of type \(Y_n^{(1)}\) for \((X,Y)=(C,D),(D,C)\) under exact monoidal functors. This can be viewed as a quantum (untwisted) affine analogue of the correspondence between irreducible oscillator and irreducible finite-dimensional representations of classical Lie algebras arising from Howe’s reductive dual pairs \((\mathfrak {g},G)\), where \(\mathfrak {g}=\mathfrak {sp}_{2n}, \mathfrak {so}_{2n}\) and \(G=O_\ell , Sp_{2\ell }\).
期刊介绍:
The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.