A q-analogue of Young symmetrizer
The author deduces a complete set of mutually orthogonal primitive idempotents of the Hecke algebra \(H=H(q)\) of the symmetric group \(S_ n\) on \(\{\) 1,...,n\(\}\), which is defined as follows, if \(\Sigma =\{\sigma_ 1,...,\sigma_{n-1}\}\) denotes the Coxeter set of elementary transpositions: H has a basis \(\{h(\pi)\}_{\pi \in S_ n}\) which is parametrized by the elements \(\pi \in S_ n\), and the multiplication is characterized by \[ (h(\sigma)+1)(h(\sigma)-q)=0,\;if\;\sigma \in \Sigma,\;h(\pi)h(\rho)=h(\pi \rho),\;if\;l(\pi)+l(\rho)=l(\pi \rho), \] where l(\(\pi)\) denotes the reduced length. H is a q-analogue of the group algebra \(C[S_ n]=H(1)\), and the resulting idempotents of \(H(q)\) yield Young's idempotents by correspondingly putting q equal to 1.
scientific article; zbMATH DE number 4049863