The Cell Structure, the Brauer Tree Structure, and Extensions of Cell Modules for Hecke Orders of Dihedral Groups

Abstract

We shall show that the Hecke order HDn of the dihedral group of order 2·pn over Z[q,q−1] for an odd prime p is a projectively cellular order. We describe the corresponding cell ideals and compute the extension groups between the corresponding cell modules; some are Z-torsion-free, some are Fp[q,q−1]-torsion-free. Moreover, we show that HDn is a Brauer tree order to the tree •——∘——• with central exceptional vertex of multiplicity pn−1·(p−1)/2.