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dc.contributor.authorCantarini, Nicoletta
dc.contributor.authorCaselli, Fabrizio
dc.contributor.authorKac, Victor
dc.date.accessioned2021-10-27T19:52:03Z
dc.date.available2021-10-27T19:52:03Z
dc.date.issued2021
dc.identifier.urihttps://hdl.handle.net/1721.1/133312
dc.description.abstract<jats:title>Abstract</jats:title><jats:p>Given a Lie superalgebra <jats:inline-formula><jats:alternatives><jats:tex-math>$${\mathfrak {g}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>g</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> with a subalgebra <jats:inline-formula><jats:alternatives><jats:tex-math>$${\mathfrak {g}}_{\ge 0}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>g</mml:mi> <mml:mrow> <mml:mo>≥</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula>, and a finite-dimensional irreducible <jats:inline-formula><jats:alternatives><jats:tex-math>$${\mathfrak {g}}_{\ge 0}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>g</mml:mi> <mml:mrow> <mml:mo>≥</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula>-module <jats:italic>F</jats:italic>, the induced <jats:inline-formula><jats:alternatives><jats:tex-math>$${\mathfrak {g}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>g</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>-module <jats:inline-formula><jats:alternatives><jats:tex-math>$$M(F)={\mathcal {U}}({\mathfrak {g}})\otimes _{{\mathcal {U}}({\mathfrak {g}}_{\ge 0})}F$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>M</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>F</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mi>U</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>g</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:msub> <mml:mo>⊗</mml:mo> <mml:mrow> <mml:mi>U</mml:mi> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>g</mml:mi> <mml:mrow> <mml:mo>≥</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:msub> <mml:mi>F</mml:mi> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> is called a finite Verma module. In the present paper we classify the non-irreducible finite Verma modules over the largest exceptional linearly compact Lie superalgebra <jats:inline-formula><jats:alternatives><jats:tex-math>$${\mathfrak {g}}=E(5,10)$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>=</mml:mo> <mml:mi>E</mml:mi> <mml:mo>(</mml:mo> <mml:mn>5</mml:mn> <mml:mo>,</mml:mo> <mml:mn>10</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> with the subalgebra <jats:inline-formula><jats:alternatives><jats:tex-math>$${\mathfrak {g}}_{\ge 0}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>g</mml:mi> <mml:mrow> <mml:mo>≥</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> of minimal codimension. This is done via classification of all singular vectors in the modules <jats:italic>M</jats:italic>(<jats:italic>F</jats:italic>). Besides known singular vectors of degree 1,2,3,4 and 5, we discover two new singular vectors, of degrees 7 and 11. We show that the corresponding morphisms of finite Verma modules of degree 1,4,7, and 11 can be arranged in an infinite number of bilateral infinite complexes, which may be viewed as “exceptional” de Rham complexes for <jats:italic>E</jats:italic>(5, 10).</jats:p>
dc.language.isoen
dc.publisherSpringer Science and Business Media LLC
dc.relation.isversionof10.1007/s00220-021-04031-z
dc.rightsCreative Commons Attribution 4.0 International license
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceSpringer
dc.titleClassification of Degenerate Verma Modules for E(5, 10)
dc.typeArticle
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematics
dc.relation.journalCommunications in Mathematical Physics
dc.eprint.versionFinal published version
dc.type.urihttp://purl.org/eprint/type/JournalArticle
eprint.statushttp://purl.org/eprint/status/PeerReviewed
dc.date.updated2021-05-21T17:27:23Z
dspace.orderedauthorsCantarini, N; Caselli, F; Kac, V
dspace.date.submission2021-05-21T17:27:24Z
mit.journal.volume385
mit.journal.issue2
mit.licensePUBLISHER_CC
mit.metadata.statusAuthority Work and Publication Information Needed


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