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), 401405
MSC (1991):
Primary 20C20
Published electronically:
September 9, 1999
MathSciNet review:
1676308
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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 SchwartzTri'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:
http://dx.doi.org/10.1090/S0002993999054246
PII:
S 00029939(99)054246
Received by editor(s):
April 10, 1998
Published electronically:
September 9, 1999
Communicated by:
Ronald M. Solomon
Article copyright:
© Copyright 1999 American Mathematical Society
