{"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}
引用次数: 0
Abstract
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.