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Abstract

It is known that the unipotent characters of GL(n,q) appearing in a given r-block (r an odd prime distinct from the defining characteristic) only depend on the order of q modulo r. We would like to give a construction of these "unipotent blocks" which doesn't involve any prime. Using the rational canonical form for elements in GL(n,q) and the degrees of the polynomials involved, we construct some blocks of unipotent characters. These blocks satisfy one implication of a generalized Nakayama Conjecture. In some cases, they satisfy both implications. Work on progress!