An explicit central element of ${\mathcal{U}}_q({\mathfrak{so}}_5)$ and its corresponding quantum Hamiltonian

Abstract

A previous paper of the author developed a general method for producing explicit central elements of quantized Lie algebras using Lusztig's inner product. This method had previously been applied for the type $C_2$, $D_3$ and $D_4$ Lie algebras. The current paper repeats the calculation for the type $B_2$ Lie algebra, which is actually isomorphic to the $C_2$ Lie algebra. The explicit expression for the corresponding quantum Hamiltonian is computed.

arXiv commentAn accessible version of this PDF is available at: https://www.math.tamu.edu/~jkuan/CentralElementB2_Accessible.pdf