{"title":"Extremal weight projectors II, 𝔤𝔩 N case","authors":"Hoel Queffelec, Paul Wedrich","doi":"10.5802/alco.330","DOIUrl":"https://doi.org/10.5802/alco.330","url":null,"abstract":"","PeriodicalId":36046,"journal":{"name":"Algebraic Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140440416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sébastien Labbé, Mélodie Lapointe, Wolfgang Steiner
{"title":"A q-analog of the Markoff injectivity conjecture holds","authors":"Sébastien Labbé, Mélodie Lapointe, Wolfgang Steiner","doi":"10.5802/alco.322","DOIUrl":"https://doi.org/10.5802/alco.322","url":null,"abstract":"","PeriodicalId":36046,"journal":{"name":"Algebraic Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139447659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We construct a natural idempotent in the descent algebra of a finite Coxeter group. The proof is uniform (independent of the classification). This leads to a simple determination of the spectrum of a natural matrix related to descents. Other applications are discussed.
{"title":"A natural idempotent in the descent algebra of a finite Coxeter group","authors":"Paul Renteln","doi":"10.5802/alco.310","DOIUrl":"https://doi.org/10.5802/alco.310","url":null,"abstract":"We construct a natural idempotent in the descent algebra of a finite Coxeter group. The proof is uniform (independent of the classification). This leads to a simple determination of the spectrum of a natural matrix related to descents. Other applications are discussed.","PeriodicalId":36046,"journal":{"name":"Algebraic Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135544990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"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.
{"title":"Jacobi–Trudi formulas and determinantal varieties","authors":"Steven V Sam, Jerzy Weyman","doi":"10.5802/alco.299","DOIUrl":"https://doi.org/10.5802/alco.299","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":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135432221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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