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Abstract |
The spectrum of a quantum integrable system is crucial to understand its properties.
R-matrices give powerful tools to study such spectra. A better understanding of
transfer-matrices obtained from R-matrices led to the proof of several results for
the corresponding quantum integrable systems. In particular, their spectra can be described
in terms of "Baxter polynomials". They appear naturally in the study of a category O of
representation of a Borel subalgebra of a quantum affine algebra.
Remarkable relations in the Grothendieck ring of this category O can be established,
from which one can derive the Bethe Ansatz equations between the roots of the Baxter
polynomials. Based on joint works with M. Jimbo, E. Frenkel and B. Leclerc. |
