Finite-dimensional modules for the quantum affine algebra Uq(g) and its borel subalgebra

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University of Wisconsin--Madison, 2007 - 61 pages
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Let n be the number of simple roots of g and choose &egr; ∈ {-1,1}n. We prove the following: (1) Let V be a finite-dimensional irreducible Uq( g )≥0-module of type &egr;. Then the action of Uq( g )≥0 on V extends uniquely to an action of Uq( g ) on V. The resulting Uq( g )-module structure on V is irreducible and of type &egr;. (2) Let V be a finite-dimensional irreducible Uq( g )-module of type &egr;. When the Uq( g )-action is restricted to Uq( g )≥0 the resulting Uq( g )≥0-module structure on V is irreducible and of type &egr;.

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