User:Alexander Chervov/Jucys Murphy elements

$$\mathbb{C} [ S_n] $$

In mathematics, Jucys-Murphy elements in the group algebra of the symmetric group are defined by the formula:


 * $$X_1=0, X_k= (1 k)+ (2 k)+...(k-1 k), k=2,...,n. $$

They play an important role in the representation theory of the symmetric group.

They generate a commutative subalgebra of C[Sk ]. Moreover, xk commutes with all elements of Sk􀀀1. The vectors of the Young basis are eigenvectors for the action of xi on V�. For any standard �-tableau U we have xi � vU = ci (U) vU; i = 1; : : : ; k: