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

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

1995-02-23

arxiv.org/abs/q-alg/9502016v1

Mathematics

Quantum Algebra

20 pages

Scientific paper

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.

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