Singular vectors of quantum group representations for straight Lie algebra roots |
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Authors: | V K Dobrev |
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Institution: | (1) Institute for Theoretical Physics, Göttingen University, Bunsenstr. 9, 3400 Göttingen, Germany |
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Abstract: | We give explicit formulae for singular vectors of Verma modules over Uq(G), where G is any complex simple Lie algebra. The vectors we present correspond exhaustively to a class of positive roots of G which we call straight roots. In some special cases, we give singular vectors corresponding to arbitrary positive roots. For our vectors we use a special basis of Uq(G
-), where G
- is the negative roots subalgebra of G, which was introducted in our earlier work in the case q=1. This basis seems more economical than the Poincaré-Birkhoff-Witt type of basis used by Malikov, Feigin, and Fuchs 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 recently introduced for other reasons by Lusztig for Uq( -), where - is a Borel subalgebra of G.A. v. Humboldt-Stiftung fellow, permanent address and after 22 September 1991: Bulgarian Academy of Sciences, Institute of Nuclear Research and Nuclear Energy, 1784 Sofia, Bulgaria. |
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Keywords: | 17B37 81R50 16W30 |
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