{"title":"Kazhdan-Lusztig-Stanley多项式的代数几何","authors":"N. Proudfoot","doi":"10.4171/EMSS/28","DOIUrl":null,"url":null,"abstract":"Kazhdan-Lusztig-Stanley polynomials are a combinatorial generalization of Kazhdan-Lusztig polynomials of for Coxeter groups that include g-polynomials of polytopes and Kazhdan-Lusztig polynomials of matroids. In the cases of Weyl groups, rational polytopes, and realizable matroids, one can count points over finite fields on flag varieties, toric varieties, or reciprocal planes to obtain cohomological interpretations of these polynomials. We survey these results and unite them under a single geometric framework.","PeriodicalId":43833,"journal":{"name":"EMS Surveys in Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2017-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/EMSS/28","citationCount":"19","resultStr":"{\"title\":\"The algebraic geometry of Kazhdan–Lusztig–Stanley polynomials\",\"authors\":\"N. Proudfoot\",\"doi\":\"10.4171/EMSS/28\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Kazhdan-Lusztig-Stanley polynomials are a combinatorial generalization of Kazhdan-Lusztig polynomials of for Coxeter groups that include g-polynomials of polytopes and Kazhdan-Lusztig polynomials of matroids. In the cases of Weyl groups, rational polytopes, and realizable matroids, one can count points over finite fields on flag varieties, toric varieties, or reciprocal planes to obtain cohomological interpretations of these polynomials. We survey these results and unite them under a single geometric framework.\",\"PeriodicalId\":43833,\"journal\":{\"name\":\"EMS Surveys in Mathematical Sciences\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2017-12-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.4171/EMSS/28\",\"citationCount\":\"19\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"EMS Surveys in Mathematical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/EMSS/28\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"EMS Surveys in Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/EMSS/28","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
The algebraic geometry of Kazhdan–Lusztig–Stanley polynomials
Kazhdan-Lusztig-Stanley polynomials are a combinatorial generalization of Kazhdan-Lusztig polynomials of for Coxeter groups that include g-polynomials of polytopes and Kazhdan-Lusztig polynomials of matroids. In the cases of Weyl groups, rational polytopes, and realizable matroids, one can count points over finite fields on flag varieties, toric varieties, or reciprocal planes to obtain cohomological interpretations of these polynomials. We survey these results and unite them under a single geometric framework.