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The first occurrence for the
irreducible modules of general linear
groups in the polynomial algebra


Authors: Pham Anh Minh and Ton That Tri
Journal: Proc. Amer. Math. Soc. 128 (2000), 401-405
MSC (1991): Primary 20C20
DOI: https://doi.org/10.1090/S0002-9939-99-05424-6
Published electronically: September 9, 1999
MathSciNet review: 1676308
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $p$ be a prime number and let $GL_{n}$ be the group of all invertible matrices over the prime field $\mathbb{F}_p$. It is known that every irreducible $GL_{n}$-module can occur as a submodule of $P$, the polynomial algebra with $n$ variables over $\mathbb{F}_p$. Given an irreducible $GL_{n}$-module $\rho $, the purpose of this paper is to find out the first value of the degree $d$ of which $\rho$ occurs as a submodule of $P_{d}$, the subset of $P$ consisting of homogeneous polynomials of degree $d$. This generalizes Schwartz-Tri's result to the case of any prime $p$.


References [Enhancements On Off] (What's this?)

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Additional Information

Pham Anh Minh
Affiliation: Department of Mathematics, College of Sciences, University of Hue, Dai hoc Khoa hoc, Hue, Vietnam
Email: paminh@bdvn.vnd.net

Ton That Tri
Affiliation: Department of Mathematics, College of Sciences, University of Hue, Dai hoc Khoa hoc, Hue, Vietnam

DOI: https://doi.org/10.1090/S0002-9939-99-05424-6
Received by editor(s): April 10, 1998
Published electronically: September 9, 1999
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1999 American Mathematical Society

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