Modular Schur functions

Walker, Grant

doi:10.1090/S0002-9947-1994-1273543-0

Modular Schur functions
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Trans. Amer. Math. Soc. 346 (1994), 569-604 Request permission

Abstract:

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

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