Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 19 (2023), 036, 13 pages      arXiv:1805.04884      https://doi.org/10.3842/SIGMA.2023.036

Explicit Central Elements of $U_q(\mathfrak{gl}(N+1))$

Jeffrey Kuan a and Keke Zhang b
a) Department of Mathematics, Texas A&M University, Mailstop 3368, College Station, TX 77843-3368, USA
b) Perimeter Institute, 31 Caroline St. N, Waterloo, ON, N2L 2Y5, Canada

Received August 25, 2022, in final form May 19, 2023; Published online June 03, 2023

Abstract
By using Drinfeld's central element construction and fusion of $R$-matrices, we construct central elements of the quantum group $U_q(\mathfrak{gl}(N+1))$. These elements are explicitly written in terms of the generators.

Key words: quantum groups; Harish-Chandra isomorphism; central elements.

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