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Teoreticheskaya i Matematicheskaya Fizika, 2019, Volume 198, Number 2, Pages 326–340
DOI: https://doi.org/10.4213/tmf9550
(Mi tmf9550)
 

This article is cited in 4 scientific papers (total in 4 papers)

Equivariant vector bundles over quantum projective spaces

A. I. Mudrov

Department of Mathematics, University of Leicester, Leicester, UK
Full-text PDF (488 kB) Citations (4)
References:
Abstract: We construct equivariant vector bundles over quantum projective spaces using parabolic Verma modules over the quantum general linear group. Using an alternative realization of the quantized coordinate ring of the projective space as a subalgebra in the algebra of functions on the quantum group, we reformulate quantum vector bundles in terms of quantum symmetric pairs. We thus prove the complete reducibility of modules over the corresponding coideal stabilizer subalgebras, via the quantum Frobenius reciprocity.
Keywords: quantum group, quantum projective space, vector bundle, symmetric pair.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-03148
This research is supported by the Russian Foundation for Basic Research (Grant No. 15-01-03148).
Received: 19.02.2018
Revised: 04.08.2018
English version:
Theoretical and Mathematical Physics, 2019, Volume 198, Issue 2, Pages 284–295
DOI: https://doi.org/10.1134/S0040577919020090
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. I. Mudrov, “Equivariant vector bundles over quantum projective spaces”, TMF, 198:2 (2019), 326–340; Theoret. and Math. Phys., 198:2 (2019), 284–295
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf9550
  • https://doi.org/10.4213/tmf9550
  • https://www.mathnet.ru/eng/tmf/v198/i2/p326
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:329
    Full-text PDF :53
    References:41
    First page:10
     
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