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.
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Funding
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.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2023, Vol. 216, pp. 405–416 https://doi.org/10.4213/tmf10458.
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Algethami, D., Mudrov, A.I. Shapovalov elements and Hasse diagrams. Theor Math Phys 216, 1255–1264 (2023). https://doi.org/10.1134/S0040577923090015
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DOI: https://doi.org/10.1134/S0040577923090015