We define generalized Koszul modules and rings develop a theory for N-graded with the degree zero part noetherian semiperfect. This specializes to classical graded artinian semisimple developed by Beilinson-Ginzburg-Soergel ungraded semiperfect Green Martinéz-Villa. Let A be left finite ring generated in 1 A0 semiperfect, J its Jacobson radical. By dual of we mean Yoneda Ext Ext_A•(A/J,A/J). If...

The HLA D/DR region of the human major histocompatibility complex encodes a family of highly polymorphic, human "Ia-like" molecules that function as genetic restriction elements in a variety of immune phenomena (1, 2). Correlations have been demonstrated between disease susceptibility and particular HLA D/DR antigens (1, 3, 4). Recent evidence (5-7) has demonstrated a considerable heterogeneity...

Let M be a finite monoid of Lie type (these are the finite analogues of linear algebraic monoids) with group of units G . The multiplicative semigroup ^AfF), where F is a finite field, is a particular example. Using HarishChandra's theory of cuspidal representations of finite groups of Lie type, we show that every complex representation of M is completely reducible. Using this we characterize t...