{"paper":{"title":"Quantum deformations of the restriction of $GL_{mn}(\\C)$-modules to $GL_m(\\C) \\times GL_n(\\C)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"B. Adsul, K. V. Subrahmanyam, M. Sohoni","submitted_at":"2009-05-01T14:28:58Z","abstract_excerpt":"In this paper, we consider the restriction of finite dimensional $GL_{mn} (\\C)$-modules to the subgroup ${GL_m (\\C)\\times GL_n (\\C)}$. In particular, for a Weyl module $V_{\\lambda} (\\C^{mn})$ of $U_q(gl_{mn})$ we construct a representation $W_{\\lambda}$ of $U_q (gl_m)\\otimes U_q (gl_n)$ such that at $q=1$, the restriction of $V_{\\lambda} (\\C^{mn})$ to $U_1 (gl_m)\\otimes U_1 (gl_n)$ matches its action on $W_{\\lambda}$ at $q=1$. Thus $W_{\\lambda}$ is a $q$-deformation of the module $V_{\\lambda}$. This is achieved by first constructing a $U_q (gl_m)\\otimes U_q (gl_n)$-module $\\wedge^k $, a $q$-de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.0094","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"}