Hecke algebras, $U_qsl_n$, and the Donald--Flanigan conjecture for $S_n$

Abstract

To each partition $\frak p$ of $n$ we associate in a canonical way a simple $S_n$ module with an orthogonal basis indexed by Young diagrams in a way which carries over immediately to the quantized case. With this we show that the Hecke algebra of $S_n$ is a global solution to the Donald--Flanigan problem for $S_n.$ The procedure gives ``canonical'' primitive idempotents different from the classical ones of Frobenius--Young and makes some number--theoretic statements.