We provide a short proof on the change-of-basis coefficients from Specht basis to Kazhdan-Lusztig basis, using theory for parabolic Hecke algebra.

In this paper we establish a strong connection between buildings and Hecke algebras by studying two algebras of averaging operators on buildings. To each locally finite regular building we associate a natural algebra B of chamber set averaging operators, and when the building is affine we also define an algebra A of vertex set averaging operators. We show that for appropriately parametrised Hec...