Canonical basis and quiver varieties

Eric Vasserot (Cergy-Pontoise)

The theory of canonical bases for modules of affine quantum algebras which do not belong to the category O is not well understood. For instance, the existence of canonical bases is still conjectural in a large extend. Moreover, there is no geometric tools analoguous to Lusztig’s construction of the canonical basis of the nilpotent part of the quantum group. In this talk we will explain a K-theoretic model for some of those bases, via quiver varieties.

References

[1] M. Kashiwara, On level zero representations of quantized affine algebras, QA/0010293.

[2] M. Varagnolo, E. Vasserot, Canonical bases and quiver varieties, RT/0107177.