Michela Varagnolo (Cergy-Pontoise)

Quantum groups and periodic modules

We give a geometric construction, via quiver varieties, of the (signed) canonical basis of an integrable module for the quantum affine algebra of type A-D-E. This construction is very similar to the Lusztig's conjectural construction of the (signed) canonical basis in the K-theory of the Springer fiber (a quiver variety in type A). We explain, for type A, how to compare the two bases in an elementary algebraic way and we point out a consequence for the periodic modules.