Codimension orbits and semi-invariants for the representations of an oriented graph of type

Author:
S. Abeasis

Journal:
Trans. Amer. Math. Soc. **282** (1984), 463-485

MSC:
Primary 14L30; Secondary 14D25, 16A64

DOI:
https://doi.org/10.1090/S0002-9947-1984-0732101-8

MathSciNet review:
732101

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Abstract: We consider the Dynkin diagram with an arbitrary orientation . For a given dimension we consider the corresponding variety of all the representations of on which a group acts naturally. In this paper we determine the maximal orbit and the codim. orbits of this action, giving explicitly their decomposition in terms of the irreducible representations of . We also deduce a set of algebraically independent semi-invariant polynomials which generate the ring of semi-invariants.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1984-0732101-8

Keywords:
Dynkin diagrams,
representations,
orbits and semi-invariants

Article copyright:
© Copyright 1984
American Mathematical Society