{"paper":{"title":"Representation theory of the nonstandard Hecke algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jonah Blasiak","submitted_at":"2012-01-10T23:55:01Z","abstract_excerpt":"The nonstandard Hecke algebra \\check{\\mathscr{H}}_r was defined by Mulmuley and Sohoni to study the Kronecker problem. We study a quotient \\check{\\mathscr{H}}_{r,2} of \\check{\\mathscr{H}}_r, called the nonstandard Temperley-Lieb algebra, which is a subalgebra of the symmetric square of the Temperley-Lieb algebra TL_r. We give a complete description of its irreducible representations. We find that the restriction of an \\check{\\mathscr{H}}_{r,2}-irreducible to \\check{\\mathscr{H}}_{r-1,2} is multiplicity-free, and as a consequence, any \\check{\\mathscr{H}}_{r,2}-irreducible has a seminormal basis "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2209","kind":"arxiv","version":2},"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"}