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... λ) have an expansion into a power series in p := q −2m(k+h∨ ) , and the sequence of these coefficients tends to 0 in the p-adic norm. Proof. This follows from the ABRR equation for the fusion matrix =-=[ES99]-=- (which in our case is equivalent the qKZ equation of Frenkel and Reshetikhin [FR92],[EFK98]). Proposition 2.2 implies that one may consider the fusion operator JV,W( ˆ λ) := JV,W(0, ˆ λ), which is a ...

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...ralised version of the gauge transformations of classical dynamical r-matrices introduced by Etingof and Varchenko in their work on the classification of classical dynamical r-matrices [19] (see also =-=[34, 17, 18, 41]-=- for further work on the classification). We summarise the relevant definitions and results from [19]. Definition 5.3 ([19]). Let G be a Lie group, H ⊂ G an abelian subgroup and r : h∗ → g⊗ g a classi...

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...trix without spectral parameter if one picks the corresponding constant coefficients. One then should correct the expression of the exchange matrix of Uq(sl2) for the standard representation found in =-=[ES99]-=- (the term q n n+1 does not appear correctly there). 3. The version of proposition 2.5 found in [EFK98] (chapter 11) does not give fusion solutions. The solutions listed there are actually our solutio...

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...Yang-Baxter equations and their solutions has many applications, including some to integrable systems and representation theory. For a recent survey of results and such applications, one can refer to =-=[21, 27]-=-. The text [24] provides a very readable introduction to the topic as well. 2.2. Definitions. Let g be a simple Lie algebra and h ⊂ g a Cartan subalgebra. The classical dynamical Yang-Baxter equation ...