On an asymptotic behavior of elements of order in irreducible representations of the classical algebraic groups with large enough highest weights

Author:
I. D. Suprunenko

Journal:
Proc. Amer. Math. Soc. **129** (2001), 2581-2589

MSC (1991):
Primary 20G05; Secondary 20G40

DOI:
https://doi.org/10.1090/S0002-9939-01-05934-2

Published electronically:
February 9, 2001

MathSciNet review:
1838380

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Abstract | References | Similar Articles | Additional Information

The behavior of the images of a fixed element of order in irreducible representations of a classical algebraic group in characteristic with highest weights large enough with respect to and this element is investigated. More precisely, let be a classical algebraic group of rank over an algebraically closed field of characteristic . Assume that an element of order is conjugate to that of an algebraic group of the same type and rank naturally embedded into . Next, an integer function on the set of dominant weights of and a constant that depend only upon , and a polynomial of degree one are defined. It is proved that the image of in the irreducible representation of with highest weight contains more than Jordan blocks of size if and are not too small and .

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Additional Information

**I. D. Suprunenko**

Affiliation:
Institute of Mathematics, National Academy of Sciences of Belarus, Surganov str. 11, Minsk, 220072, Belarus

Email:
suprunenko@im.bas-net.by

DOI:
https://doi.org/10.1090/S0002-9939-01-05934-2

Keywords:
Classical groups,
representations,
Jordan blocks

Received by editor(s):
January 24, 2000

Published electronically:
February 9, 2001

Additional Notes:
This research has been supported by the Institute of Mathematics of the National Academy of Sciences of Belarus in the framework of the State program “Mathematical structures” and by the Belarus Basic Research Foundation, Project F98-180.

Communicated by:
Stephen D. Smith

Article copyright:
© Copyright 2001
American Mathematical Society