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Moreover, the decomposition in the ± direct sum of generalized eigenspaces of operators φi,n does not depend on z, because ± the action of φi,n on V and on V (z) differs only by scalar factors zn . In particular, ± BV is also a Jordan basis for φi,n acting on V (z) for all z ∈ C× . 3. 3 ([FR2]). 4) as elements of C[[u±1 ]], where Qi (u), Ri (u) are polynomials in u with constant term 1. of Now we can relate the monomials appearing in χq (V ) to the common eigenvalues ± i (u) on V . 4. Let V be a finite-dimensional Uq g-module.

In this section we prove that the reducibility of a tensor product of the fundamental representations is always caused by a pole in the R-matrix. We say that a monomial m has positive lattice support with base a if m is a product ±1 Yi,aq n with n ≥ 0. 1. All monomials in χq (Vωi (a)) have positive lattice support with base a. Proof. 2) for χq (V1 (a)). The q-character of any irreducible representation V of Uq sl2 is a subsum of a product of the q-characters of V1 (b)’s. Moreover, this subsum includes the highest monomial.

Minimal affinizations of representations of quantum groups: The simply laced case. J. Algebra 184, no. : Yangians: their representations and characters. Representations of Lie groups, Lie algebras and their quantum analogues. Acta Appl. Math. 44, no. : La R-matrice pour les algebres quantiques de type affine non tordu. Ann. Sci. Ecole Norm. Sup. 31, no. : Hopf algebras and the quantum Yang–Baxter equation. Sov. Math. Dokl. : A new realization of Yangians and of quantum affine algebras. Sov. Math.