Quantum group \(U_q(A_\ell)\) singular vectors in Poincaré-Birkhoff-Witt basis (Q1819179)

A singular vector of a Verma module is a non-zero element, annihilated by the positive part of the universal enveloping algebra. In this letter the authors give an explicit expression for singular vectors in Verma modules over the Drinfeld-Jimbo quantum algebra \(U_q(A_l)\) in terms of the Poincaré-Birkhoff-Witt basis and relate them with the expression for these vectors in terms of simple root vectors, obtained by the first author earlier.