{"paper":{"title":"Geometric Complexity Theory IV: nonstandard quantum group for the Kronecker problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Jonah Blasiak, Ketan D. Mulmuley, Milind Sohoni","submitted_at":"2007-03-22T15:35:29Z","abstract_excerpt":"The Kronecker coefficient g_{\\lambda \\mu \\nu} is the multiplicity of the GL(V)\\times GL(W)-irreducible V_\\lambda \\otimes W_\\mu in the restriction of the GL(X)-irreducible X_\\nu via the natural map GL(V)\\times GL(W) \\to GL(V \\otimes W), where V, W are \\mathbb{C}-vector spaces and X = V \\otimes W. A fundamental open problem in algebraic combinatorics is to find a positive combinatorial formula for these coefficients.\n  We construct two quantum objects for this problem, which we call the nonstandard quantum group and nonstandard Hecke algebra. We show that the nonstandard quantum group has a comp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0703110","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}