  We initiate the systematic study of endomorphism algebras of permutation
modules and show they are obtainable by a descent from a certain "generic"
Hecke algebra, infinite-dimensional in general, coming from the universal
enveloping algebra of gl_n (or sl_n). The endomorphism algebras and the generic
algebras are cellular. We give several equivalent descriptions of these
algebras, find a number of explicit bases, and describe indexing sets for their
irreducible representations.
