Integral Hecke Algebras for Finite Generalized Polygons


Hacioglu I.

ALGEBRA COLLOQUIUM, vol.18, no.2, pp.259-272, 2011 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 2
  • Publication Date: 2011
  • Doi Number: 10.1142/s1005386711000162
  • Journal Name: ALGEBRA COLLOQUIUM
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.259-272

Abstract

Suppose that (P, B, F) is a triple consisting of the points, blocks and flags of a generalized m-gon, and H(F) the associated rank-2 Iwahori-Hecke algebra. H(F) acts naturally on the integral standard module ZF based on F. This work gives arithmetic conditions on a subring R, where R contains the integers and is contained in the rationals, that insure the associated R-ary Iwahori-Hecke algebra to be completely reducible on RF. The constituent multiplicities are related to the R-normal form of the incidence matrix of (P, B, F).