{"paper":{"title":"Commuting difference operators and the combinatorial Gale transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"I. Krichever","submitted_at":"2014-03-18T22:09:49Z","abstract_excerpt":"We study the spectral theory of $n$-periodic strictly triangular difference operators $L=T^{-k-1}+\\sum_{j=1}^k a_i^j T^{-j}$ and the spectral theory of the \"superperiodic\" operators for which all solutions of the equation $(L+1)\\psi=0$ are (anti)periodic. We show that for a superperiodic operator $L$ there exists a unique superperiodic operator ${\\cal L}$ of order $(n-k-1)$ which commutes with $L$ and show that the duality $L\\leftrightarrow {\\cal L}$ coincides up to a certain involution with the combinatorial Gale transform recently introduced in [21]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4629","kind":"arxiv","version":1},"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"}