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A Classification of Multiplicity Free Actions

✍ Scribed by Chal Benson; Gail Ratcliff

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
374 KB
Volume
181
Category
Article
ISSN
0021-8693

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✦ Synopsis

The action of a complex algebraic group G on an affine variety V is said to be multiplicity free if each irreducible representation of G occurs at most once in the w x ring ‫ރ‬ V of regular functions on V. This paper concerns the classical setting where V is a vector space and G acts linearly on V. The irreducible linear multiplicity free actions have been classified by V. Kac. The focus here is on nonirreducible linear multiplicity free actions. We exhibit many such actions which do not decompose as direct products of irreducible actions. Our main results provide a classification for all linear multiplicity free actions on a vector space.

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