dorsal/arxiv
View SchemaOn q-Analogues of Bounded Symmetric Domains and Dolbeault Complexes
| Authors | S. Sinel'shchikov, L. Vaksman |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9703005 |
| URL | https://arxiv.org/abs/q-alg/9703005 |
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 .
{
"annotation_id": "1def2dc7-3656-4c86-9832-dbe7de2b850b",
"date_created": "2026-03-02T18:01:28.649000Z",
"date_modified": "2026-03-02T18:01:28.649000Z",
"file_hash": "45e9b5fa3f08dfc9d7acfc9cee2659958be2867e34f617020ce5eb7f16f94e84",
"private": false,
"record": {
"abstract": "A very well known result by Harish-Chandra claims that any Hermitian\nsymmetric space of non-compact type admits a canonical embedding into a complex\nvector space $V$. The image of this embedding is a bounded symmetric domain in\n$V$. This work provides a construction of q-analogues of a polynomial algebra\non $V$ and the differential algebra of exterior forms on $V$. A way of\nproducing a q-analogue of the bounded function algebra in a bounded symmetric\ndomain is described. All the constructions are illustrated by detailed\ncalculations in the case of the simplest Hermitian symmetric space\n$SU(1,1)/U(1)$. The development of these ideas can be found in math.QA/9803110\nand math.QA/9809038 .",
"arxiv_id": "q-alg/9703005",
"authors": [
"S. Sinel\u0027shchikov",
"L. Vaksman"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "On q-Analogues of Bounded Symmetric Domains and Dolbeault Complexes",
"url": "https://arxiv.org/abs/q-alg/9703005"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "cdba1591-9a2e-4bef-9175-752237976ac5",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}