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Teoreticheskaya i Matematicheskaya Fizika, 2023, Volume 216, Number 3, Pages 405–416
DOI: https://doi.org/10.4213/tmf10458 (Mi tmf10458) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Shapovalov elements and Hasse diagrams

D. Algethamiab, A. I. Mudrovac

a University of Leicester, Leicester, United Kingdom
b University of Bisha, Bisha, Saudi Arabia
c Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow region, Russia
Full-text PDF (489 kB) Citations (2)
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DOI: https://doi.org/10.4213/tmf10458
Abstract: Shapovalov elements of quantum groups are special polynomials in negative simple root vectors with coefficients in the rational Cartan subalgebra that relate singular vectors in reducible Verma modules with their highest vectors. We give explicit expressions for Shapovalov elements of nonexceptional quantum groups in terms of matrix elements of quantum L-operators using calculations on Hasse diagrams associated with auxiliary representations.
Keywords: Shapovalov elements, R-matrix, Verma modules, Hasse diagrams.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FSMG-2023-0013
075-15-2022-289
University of Bisha, Bisha, Saudi Arabia
This work was done at the Center of Pure Mathematics, MIPT. It also was supported in part by the Ministry of Science and Higher Education of the Russian Federation (agreement No. 075-15-2022-289). D. Algethami is thankful to the Deanship of Scientific Research at the University of Bisha for financial support through the Scholarship Program of the University.
Received: 31.01.2023
Revised: 31.01.2023
English version:
Theoretical and Mathematical Physics, 2023, Volume 216, Issue 3, Pages 1255–1264
DOI: https://doi.org/10.1134/S0040577923090015
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: D. Algethami, A. I. Mudrov, “Shapovalov elements and Hasse diagrams”, TMF, 216:3 (2023), 405–416; Theoret. and Math. Phys., 216:3 (2023), 1255–1264
Citation in format AMSBIB
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\by D.~Algethami, A.~I.~Mudrov
\paper Shapovalov elements and Hasse diagrams
\jour TMF
\yr 2023
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\issue 3
\pages 405--416
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\transl
\jour Theoret. and Math. Phys.
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\issue 3
\pages 1255--1264
\crossref{https://doi.org/10.1134/S0040577923090015}
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  • https://www.mathnet.ru/eng/tmf10458
  • https://doi.org/10.4213/tmf10458
  • https://www.mathnet.ru/eng/tmf/v216/i3/p405
    • This publication is cited in the following 2 articles:
    1. Andrey Mudrov, “Shapovalov elements of classical and quantum groups”, Journal of Pure and Applied Algebra, 228:7 (2024), 107634  crossref  mathscinet
    2. N. V. Kryazhevskikh, A. I. Mudrov, “Root vectors in quantum groups”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 30, Zap. nauchn. sem. POMI, 532, POMI, SPb., 2024, 212–234  mathnet
    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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