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 H-Dn of the dihedral group of order 2 .p (n) over Z[q, q(-1)] for an odd prime p is a projectively cellular order. W e describe the corresponding cell ideals and compute the extension groups b etween the corresponding cell modules; some are Z-torsion-free, some are F- p[q, q(-1)]-torsion-free. Moreover, we show that H-Dn is a Brauer tree orde r to the tree with central exceptional vertex of multiplicity p(n-1). (p - 1)/2. (C) 2001 Academic Press.