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Capelli eigenvalue problem for Lie superalgebras and supersymmetric polynomials

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Authors : Serganova, Vera (Author of the conference)
CIRM (Publisher )

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Abstract : We study invariant differential operators on representations of supergroups associated with simple Jordan superalgebras, in the classical case this problem goes back to Kostant. Eigenvalues of Capelli differential operators give interesting families of polynomials such as super Jack polynomials of Sergeev and Veselov and factorial Schur polynomials of Okounkov and Ivanov. We also discuss connection with deformed Calogero-Moser systems in the super case.

Keywords : Lie superalgebras; Capelli problem; super Jack polynomials; shifted super Jack polynomials

MSC Codes :
17A70 - Superalgebras
 17B10 - Representations of Lie algebras, algebraic theory
 17B60 - Lie (super)algebras associated with other structures (associative, Jordan, etc.)
 81T60 - Supersymmetric field theories
Additional resources :
https://www.cirm-math.fr/ProgWeebly/Renc1746/Serganova.pdf
    Information on the Video

    Language : English
    Available date : 07/06/2018
    Conference Date : 07/06/2018
    Subseries : Research talks
    arXiv category : Representation Theory ; Mathematical Physics
    Mathematical Area(s) : Algebra ; Mathematical Physics
    Format : MP4 (.mp4) - HD
    Video Time : 00:55:53
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2018-06-07_Serganova.mp4
Information on the Event

Event Title : Representation theory, mathematical physics and integrable systems / Théorie des représentations, physique mathématique et systèmes intégrables
Event Organizers : Yakimov, Milen ; Webster, Ben
Dates : 04/06/2018 - 08/06/2018
Event Year : 2018
Event URL : https://conferences.cirm-math.fr/1746.html

Citation Data

DOI : 10.24350/CIRM.V.19415203
Cite this video as: Serganova, Vera (2018). Capelli eigenvalue problem for Lie superalgebras and supersymmetric polynomials. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19415203
URI : http://dx.doi.org/10.24350/CIRM.V.19415203

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