2008/05/08 by Kentaro Wada, Wada, Kentaro
Mathematics · #20C08 #20C20 #20G05 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:20C08 #msc:20C20 #msc:20G05
paper · pdf · doi:10.48550/arxiv.0805.1147
37pages
arxiv created 2008/05/08 · arxiv updated 2009/12/01
For a cellular algebra \A with a cellular basis \ZC, we consider a decomposition of the unit element 1_\A into orthogonal idempotents (not necessary primitive) satisfying some conditions. By using this decomposition, the cellular basis \ZC can be partitioned into some pieces with good properties. Then by using a certain map \a, we give a coarse partition of \ZC whose refinement is the original partition. We construct a Levi type subalgebra \aA of \A and its quotient algebra \oA, and also construct a parabolic type subalgebra \tA of \A, which contains \aA with respect to the map \a. Then, we study the relation of standard modules, simple modules and decomposition numbers among these algebras. Finally, we study the relationship of blocks among these algebras.