Geometric Complexity Theory Iv : Nonstandard Quantum Group for the Kronecker Problem

@inproceedings{Blasiak2011GeometricCT,
title={Geometric Complexity Theory Iv : Nonstandard Quantum Group for the Kronecker Problem},
author={Jonah Blasiak and Ketan Mulmuley and Milind A. Sohoni},
year={2011}
}

The Kronecker coefficient gλμν is the multiplicity of the GL(V )×GL(W )irreducible Vλ ⊗Wμ in the restriction of the GL(X)-irreducible Xν via the natural map GL(V )×GL(W )→ GL(V ⊗W ), where V,W are C-vector spaces and X = V ⊗W . A fundamental open problem in algebraic combinatorics is to find a positive combinatorial formula for these coefficients. We construct two quantum objects for this problem, which we call the nonstandard quantum group and nonstandard Hecke algebra. We show that the… CONTINUE READING