$G_2$ representations and semistandard tableaux
William M. McGovern
TL;DR
This paper develops a tableau-based realization of irreducible finite-dimensional representations of the complex Lie group of type G2, providing explicit generators for the defining ideal of the flag variety.
Contribution
It introduces a novel tableau model for G2 representations and explicitly describes the ideal generators of the associated flag variety.
Findings
Realization of G2 representations via tableaux
Explicit generators of the flag variety's defining ideal
Extension of previous work on Lie group representations
Abstract
Continuing earlier work, we show how to realize irreducible finite-dimensional representations of the complex group of type via tableaux, along the way exhibiting explicit generators of the defining ideal of the flag variety
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Polynomial and algebraic computation