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

We shall show that the Hecke order Dn of the dihedral group of order 2 • pn over [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 -torsion-free, some are p[q, q− 1]-torsion-free. Moreover, we show that Dn is a Brauer tree order to the tree •—— ——• with central exceptional vertex of multiplicity pn − 1 • (p − 1)/2.