{"title":"Jacobi-Trudi公式与行列式","authors":"Steven V Sam, Jerzy Weyman","doi":"10.5802/alco.299","DOIUrl":null,"url":null,"abstract":"Gessel gave a determinantal expression for certain sums of Schur functions which visually looks like the classical Jacobi–Trudi formula. We explain the commonality of these formulas using a construction of Zelevinsky involving BGG complexes and use this explanation to generalize this formula in a few different directions.","PeriodicalId":36046,"journal":{"name":"Algebraic Combinatorics","volume":"48 30","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Jacobi–Trudi formulas and determinantal varieties\",\"authors\":\"Steven V Sam, Jerzy Weyman\",\"doi\":\"10.5802/alco.299\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Gessel gave a determinantal expression for certain sums of Schur functions which visually looks like the classical Jacobi–Trudi formula. We explain the commonality of these formulas using a construction of Zelevinsky involving BGG complexes and use this explanation to generalize this formula in a few different directions.\",\"PeriodicalId\":36046,\"journal\":{\"name\":\"Algebraic Combinatorics\",\"volume\":\"48 30\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebraic Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5802/alco.299\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebraic Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/alco.299","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
Gessel gave a determinantal expression for certain sums of Schur functions which visually looks like the classical Jacobi–Trudi formula. We explain the commonality of these formulas using a construction of Zelevinsky involving BGG complexes and use this explanation to generalize this formula in a few different directions.
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