{"paper":{"title":"Representations of affine Lie algebras, parabolic differential equations, and Lame functions","license":"","headline":"","cross_cats":["math.CA","math.QA"],"primary_cat":"hep-th","authors_text":"Alexander Kirillov Jr, Pavel Etingof","submitted_at":"1993-10-14T15:19:41Z","abstract_excerpt":"We consider correlation functions for the Wess-Zumino-Witten model on the torus with the insertion of a Cartan element; mathematically this means that we consider the function of the form $F=\\Tr (\\Phi_1 (z_1)\\ldots \\Phi_n (z_n)q^{-\\d}e^{h})$ where $\\Phi_i$ are intertwiners between Verma modules and evaluation modules over an affine Lie algebra $\\ghat$, $\\d$ is the grading operator in a Verma module and $h$ is in the Cartan subalgebra of $\\g$. We derive a system of differential equations satisfied by such a function. In particular, the calculation of $q\\frac{\\d} {\\d q} F$ yields a parabolic sec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9310083","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"}