V K Dobrev 1992 J. Phys. A: Math. Gen. 25 149 doi:10.1088/0305-4470/25/1/019
V K Dobrev
Show affiliationsThe author gives explicit formulae for singular vectors of Verma modules over Uq(G). They give the general formula for G=An, for some cases when G=Dn and for some rank-two subalgebras of G not=An, Dn. For this he uses a special basis of Uq(G-), where G- is the negative root subalgebra of G, which was introduced in his earlier work on the case q=1. This basis seems more economical than the Poincare-Birkhoff-Witt type of basis used by Malikov, Feigin and Fuchs (1986) for the construction of singular vectors of Verma modules in the case q=1. Furthermore this basis turns out to be part of a general basis introduced recently for other reasons by Lusztig (1988) for Uq(B-), where B- is a Borel subalgebra of G.
81R50 Quantum groups and related algebraic methods (See also 16W35, 17B37)
Issue 1 (7 January 1992)
V K Dobrev 1992 J. Phys. A: Math. Gen. 25 149
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