HECKE ALGEBRAS, U(Q)SL(N), AND THE DONALD-FLANIGAN CONJECTURE FOR S-N

The Donald-Flanigan conjecture asserts that the integral group ring ZG of a finite group G can be deformed to an algebra A over the power se ries ring Z[[t]] with underlying module ZG[[t]] such that if p is any prime dividing #G then A x(Z[[t]]) <(F-p((t)))over bar> is a direct su m of total matric algebras whose blocks are in natural bijection with and of the same dimensions as those of CG. We prove this for G = S-n u sing the natural representation of its Hecke algebra 7-1 by quantum Ya ng-Baxter matrices to show that over Z[q] localized at the multiplicat ively closed set generated by q and all i(q2) = 1+q(2)+q(4)+...+q(2(i- 1)), i = 1, 2,..., n, the Hecke algebra becomes a direct sum of total matric algebras. The corresponding ''canonical'' primitive idempotents are distinct from Wenzl's and in the classical case (q = 1), from tho se of Young.