Modular Schur functions

Source abstract

A new family of symmetric functions is considered. These functions are analogous to the classical Schur functions, but depend on an integer modulus p ⩾ 2 p \geqslant 2 , as well as on a partition λ \lambda . In the case where p p is prime, certain of these functions are shown to be irreducible characters of the general linear group G L ( n , K ) GL(n,K) in the natural characteristic p p of the field K K . This dualises a wellknown criterion of G. D. James for such characters to be given by classical Schur functions.