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A study of the representations supported by the orbit closure of the determinant

Part of: Affine geometry Algorithms - Computer Science Lie groups Algebraic groups Linear algebraic groups and related topics

Published online by Cambridge University Press:  24 October 2014

Shrawan Kumar
Shrawan Kumar*
Affiliation:
Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599-3250, USA email shrawan@email.unc.edu
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Abstract

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We show the existence of a large family of representations supported by the orbit closure of the determinant. However, the validity of our result is based on the validity of the celebrated ‘Latin square conjecture’ due to Alon and Tarsi or, more precisely, on the validity of an equivalent ‘column Latin square conjecture’ due to Huang and Rota.

Keywords

determinant orbit closureLatin squaresAlon–Tarsi conjecturegeometric complexity theoryValiant’s conjecturerepresentations

MSC classification

Primary: 14L30: Group actions on varieties or schemes (quotients) 14L24: Geometric invariant theory 14R20: Group actions on affine varieties 20G05: Representation theory 22E46: Semisimple Lie groups and their representations 68W30: Symbolic computation and algebraic computation
Type
Research Article
Information
Compositio Mathematica , Volume 151 , Issue 2 , February 2015 , pp. 292 - 312
Copyright
© The Author 2014 

References

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