Double affine Hecke algebras and affine Springer fibers

Eric Vasserot

In this talk, we will review the geometric construction of the double affine Hecke algebra via affine Spinger fibers. Special attention will be given to type A and the link with quantum affine Schur algebras. Applications (conjectural) to representation theory of p-adic groups in positive (non residual) characteristic will be explained. Finally, we will recall some analogies with punctual Hilbert schemes in type A.