Joseph-like ideals and harmonic analysis for $osp(m|2n)$

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10191635" target="_blank" >RIV/00216208:11320/13:10191635 - isvavai.cz</a>
Result on the web
<a href="http://imrn.oxfordjournals.org/content/early/2013/04/22/imrn.rnt074.abstract" target="_blank" >http://imrn.oxfordjournals.org/content/early/2013/04/22/imrn.rnt074.abstract</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/imrn/rnt074" target="_blank" >10.1093/imrn/rnt074</a>

Result language
angličtina
Original language name
Joseph-like ideals and harmonic analysis for $osp(m|2n)$
Original language description
The Joseph ideal in the universal enveloping algebra Graphic is the annihilator ideal of the Graphic-representation on the harmonic functions on Graphic. The Joseph ideal for Graphic is the annihilator ideal of the Segal-Shale-Weil (metaplectic) representation. Both ideals can be constructed in a unified way from a quadratic relation in the tensor algebra Graphic for Graphic equal to Graphic or Graphic. In this paper, we construct two analogous ideals in Graphic and Graphic for Graphic the orthosymplectic Lie super-algebra Graphic and prove that they have unique characterizations that naturally extend the classical case. Then we show that these two ideals are the annihilator ideals of, respectively, the Graphic-representation on the spherical harmonicson Graphic and a generalization of the metaplectic representation to Graphic. This proves that these ideals are reasonable candidates to establish the theory of Joseph-like ideals for Lie super-algebras. We also discuss the relation betw
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Eduard Čech Institute for algebra, geometry and mathematical physics</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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