{"title":"图连接上的量子超可积自旋系统","authors":"Nicolai Reshetikhin, Jasper Stokman","doi":"10.1016/j.indag.2024.03.008","DOIUrl":null,"url":null,"abstract":"In this paper we construct certain quantum spin systems on moduli spaces of -connections on a connected oriented finite graph, with a simply connected compact Lie group. We construct joint eigenfunctions of the commuting quantum Hamiltonians in terms of local invariant tensors. We determine sufficient conditions ensuring superintegrability of the quantum spin system using irreducibility criteria for Harish-Chandra modules due to Harish-Chandra and Lepowsky & McCollum. The resulting class of quantum superintegrable spin systems includes the quantum periodic and open spin Calogero–Moser spin chains as special cases. In the periodic case the description of the joint eigenfunctions in terms of local invariant tensors are multipoint generalized trace functions, in the open case multipoint spherical functions on compact symmetric spaces.","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":"9 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quantum superintegrable spin systems on graph connections\",\"authors\":\"Nicolai Reshetikhin, Jasper Stokman\",\"doi\":\"10.1016/j.indag.2024.03.008\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we construct certain quantum spin systems on moduli spaces of -connections on a connected oriented finite graph, with a simply connected compact Lie group. We construct joint eigenfunctions of the commuting quantum Hamiltonians in terms of local invariant tensors. We determine sufficient conditions ensuring superintegrability of the quantum spin system using irreducibility criteria for Harish-Chandra modules due to Harish-Chandra and Lepowsky & McCollum. The resulting class of quantum superintegrable spin systems includes the quantum periodic and open spin Calogero–Moser spin chains as special cases. In the periodic case the description of the joint eigenfunctions in terms of local invariant tensors are multipoint generalized trace functions, in the open case multipoint spherical functions on compact symmetric spaces.\",\"PeriodicalId\":501252,\"journal\":{\"name\":\"Indagationes Mathematicae\",\"volume\":\"9 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indagationes Mathematicae\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1016/j.indag.2024.03.008\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1016/j.indag.2024.03.008","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Quantum superintegrable spin systems on graph connections
In this paper we construct certain quantum spin systems on moduli spaces of -connections on a connected oriented finite graph, with a simply connected compact Lie group. We construct joint eigenfunctions of the commuting quantum Hamiltonians in terms of local invariant tensors. We determine sufficient conditions ensuring superintegrability of the quantum spin system using irreducibility criteria for Harish-Chandra modules due to Harish-Chandra and Lepowsky & McCollum. The resulting class of quantum superintegrable spin systems includes the quantum periodic and open spin Calogero–Moser spin chains as special cases. In the periodic case the description of the joint eigenfunctions in terms of local invariant tensors are multipoint generalized trace functions, in the open case multipoint spherical functions on compact symmetric spaces.