Vyjayanthi Chari

Quantum affine algebras

AbstractWe classify the finite-dimensional irreducible representations of the quantum affine algebra

On the fermionic formula and the Kirillov-Reshetikhin conjecture

U_q (\hat sl_2 )

Quantum affine algebras at roots of unity

in terms of highest weights (this result has a straightforward generalization for arbitrary quantum affine algebras). We also give an explicit construction of all such representations by means of an evaluation homomorphism

Yangians, integrable quantum systems and Dorey's rule

U_q (\hat sl_2 ) \to U_q (sl_2 )

Integrable representations of twisted affine Lie algebras

, first introduced by M. Jimbo. This is used to compute the trigonometricR-matrices associated to finite-dimensional representations of