Date: 27 May 2005

Quantum R matrix related to the generalized Toda system: An algebraic approach

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We report on some recent progress concerning the Yang-Baxter equation and related algebraic structures -the q-analogue of the universal enveloping algebra and the Hecke algebra. The results include 1) construction of trigonometric R matrices related to the vector representation of non-exceptional Lie algebras, ii) construction of representations of for , and iii) existence of R for a class of representations of .