Chapter

Field Theory, Quantum Gravity and Strings

Volume 246 of the series Lecture Notes in Physics pp 335-361

Date:

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

  • Michio JimboAffiliated withResearch Institute for Mathematical Sciences, Kyoto University

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Abstract

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
.