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On q-Analogues of Bounded Symmetric Domains and Dolbeault Complexes

S. Sinel'shchikov·L. Vaksman
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Abstract

A very well known result by Harish-Chandra claims that any Hermitian symmetric space of non-compact type admits a canonical embedding into a complex vector space $V$. The image of this embedding is a bounded symmetric domain in $V$. This work provides a construction of q-analogues of a polynomial 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 bounded symmetric domain is described. All the constructions are illustrated by detailed calculations in the case of the simplest Hermitian symmetric space $SU(1,1)/U(1)$. The development of these ideas can be found in math.QA/9803110 and math.QA/9809038 .

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BibTeXRIS

S. Sinel'shchikov, L. Vaksman. 1998-09-18. On q-Analogues of Bounded Symmetric Domains and Dolbeault Complexes. https://arxiv.org/abs/q-alg/9703005

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