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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Modular Schur functions


Author: Grant Walker
Journal: Trans. Amer. Math. Soc. 346 (1994), 569-604
MSC: Primary 20C20; Secondary 20C30, 20G15
MathSciNet review: 1273543
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1273543-0
PII: S 0002-9947(1994)1273543-0
Article copyright: © Copyright 1994 American Mathematical Society