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 be a prime number and let be the group of all invertible matrices over the prime field . It is known that every irreducible -module can occur as a submodule of , the polynomial algebra with variables over . Given an irreducible -module , the purpose of this paper is to find out the first value of the degree of which occurs as a submodule of , the subset of consisting of homogeneous polynomials of degree . This generalizes Schwartz-Tri's result to the case of any prime .

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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