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Infinite dimensional representations of

Published online by Cambridge University Press:  18 May 2009

A. Dean  and
F. Zorzitto
A. Dean
Affiliation:
Department of MathematicsBishop's University Lennoxville, QuebecCanadaJim 1Z7
F. Zorzitto
Affiliation:
Department of Pure MathematicsUniversity of WaterlooWaterloo, OntarioCanadaN2L 3G1
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By a representation of the extended Dynkin diagram we shall mean a list of 5 vector spaces P, E1, E2, E3, E4 over an algebraically closed field K, and 4 linear maps a1, a2, a3, a4 as shown.

The spaces need not be of finite dimension.

In their solution of the 4-subspace problem [6], Gelfand and Ponomarev have classified such representations when the spaces are finite dimensional. A representation like (1) can also be viewed as a module over the K-algebra R4 consisting of all 5 × 5 matrices having zeros off the first row and off the main diagonal.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 32 , Issue 1 , January 1990 , pp. 25 - 33
Copyright
Copyright © Glasgow Mathematical Journal Trust 1990

References

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