On the new generators of the Hecke algebra \({\mathcal H}(G,U,\mathbf{1})\)
The object of this paper is to define Fourier-Grassmann operators for a simple Chevalley group \(G\), and to show that these operators represent the braid group associated to the Weyl group of \(G\). Moreover, they define together with homothetic operators a presentation of a Hecke algebra. In the case where the Cartan matrix of \(G\) is symmetric a construction of a representation module \(\varphi\) of the Weyl group \(W\) of \(G\) is given, and a correspondence in \(\varphi\) between generalized Steinberg representations and certain representations of the semidirect product \(W\ltimes T\), where \(T\) is a maximal torus of a Borel subgroup of \(G\).
scientific article; zbMATH DE number 1218687
scientific article