{"title":"标准单项式理论在特征二上模Frobenius","authors":"Laura Casabella , Teresa Yu","doi":"10.1016/j.jpaa.2025.108051","DOIUrl":null,"url":null,"abstract":"<div><div>Over a field of characteristic two, we develop a theory of standard monomials for polynomial rings modulo a Frobenius power of the maximal ideal generated by all variables. As a result, we obtain a filtration by modular <span><math><msub><mrow><mi>GL</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>-representations whose characters are given by particular truncated Schur polynomials, thus proving a conjecture by Gao–Raicu–VandeBogert in the characteristic two case.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 9","pages":"Article 108051"},"PeriodicalIF":0.8000,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Standard monomial theory modulo Frobenius in characteristic two\",\"authors\":\"Laura Casabella , Teresa Yu\",\"doi\":\"10.1016/j.jpaa.2025.108051\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Over a field of characteristic two, we develop a theory of standard monomials for polynomial rings modulo a Frobenius power of the maximal ideal generated by all variables. As a result, we obtain a filtration by modular <span><math><msub><mrow><mi>GL</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>-representations whose characters are given by particular truncated Schur polynomials, thus proving a conjecture by Gao–Raicu–VandeBogert in the characteristic two case.</div></div>\",\"PeriodicalId\":54770,\"journal\":{\"name\":\"Journal of Pure and Applied Algebra\",\"volume\":\"229 9\",\"pages\":\"Article 108051\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2025-07-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Pure and Applied Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022404925001902\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Pure and Applied Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022404925001902","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Standard monomial theory modulo Frobenius in characteristic two
Over a field of characteristic two, we develop a theory of standard monomials for polynomial rings modulo a Frobenius power of the maximal ideal generated by all variables. As a result, we obtain a filtration by modular -representations whose characters are given by particular truncated Schur polynomials, thus proving a conjecture by Gao–Raicu–VandeBogert in the characteristic two case.
期刊介绍:
The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.