  P. Deligne defined interpolations of the tensor category of representations
of the symmetric group S_n to complex values of n. Namely, he defined tensor
categories Rep(S_t) for any complex t. This construction was generalized by F.
Knop to the case of wreath products of S_n with a finite group. Generalizing
these results, we propose a method of interpolating representations categories
of various algebras containing S_n (such as degenerate affine Hecke algebras,
symplectic reflection algebras, rational Cherednik algebras, etc.) to complex
values of n. We also define the group algebra of S_n for complex n, study its
properties, and propose a Schur-Weyl duality for Rep(S_t). In version 2, same
more details have been added.
