広島大学総合科学部紀要. IV, 理系編 Volume 20
published_at 1994-12-28

Invariant subvarieties of the 3-tensor space C^2⨂C^2⨂C^2

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Abstract
We classify G-invariant subvarieties of the 3-tensor space C^2⨂C^2⨂C^2 that are defined by polynomials with degree≤6,where G=GL(2,C)×GL(2,C)×GL(2,C). We also calculate the character fo S^p(C^2⨂C^2⨂C^2), determine the generators of each irreducible component of S^p(C^2⨂C^2⨂C^2), and obtain some curious identities between them that play a fundamental role in classifying invariant subvarieties.
Keywords
3-tensor space
variety
invariant
representation
character
Schur function