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On q-Analogues of Bounded Symmetric Domains and Dolbeault Complexes

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Abstract

A very well known result by Harish-Chandra claims that any Hermitiansymmetric space of non-compact type admits a canonical embedding into acomplex vector space V. The image of this embedding is a bounded symmetricdomain in V. This work provides a construction of q-analogues of apolynomial algebra on V and the differential algebra of exterior forms on V.A way of producing a q-analogue of the bounded function algebra in a boundedsymmetric domain is described. All the constructions are illustrated bydetailed calculations in the case of the simplest Hermitian symmetric spaceSU (1,1)/U(1).

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Authors and Affiliations

  1. Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Kharkov, Ukraine

    S. Sinel’shchikov & L. Vaksman

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  1. S. Sinel’shchikov
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  2. L. Vaksman
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Sinel’shchikov, S., Vaksman, L. On q-Analogues of Bounded Symmetric Domains and Dolbeault Complexes. Mathematical Physics, Analysis and Geometry 1, 75–100 (1998). https://doi.org/10.1023/A:1009704002239

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  • DOI: https://doi.org/10.1023/A:1009704002239

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