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Singular vectors of representations of quantum groups

V K Dobrev

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The 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.


PACS

02.20.Uw Quantum groups

02.10.De Algebraic structures and number theory

03.65.Fd Algebraic methods

MSC

81R50 Quantum groups and related algebraic methods (See also 16W35, 17B37)

22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (See also 17B10)

Subjects

Mathematical physics

Quantum information and quantum mechanics

Dates

Issue 1 (7 January 1992)



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