{"title":"一些开放理查德森品种上的单项式分类法","authors":"Yingjin Bi","doi":"arxiv-2409.04715","DOIUrl":null,"url":null,"abstract":"In this paper, we investigate the cluster morphisms between cluster algebras\nand the functor of monoidal categories. Our findings demonstrate that there\nexists a monoidal categorification of the coordinate ring of the open\nRichardson variety $\\mathcal{R}_{w,v}$, where $w=vu$ and\n$\\ell(w)=\\ell(u)+\\ell(v)$. This result confirms a conjecture proposed by\nKashiwara, Kim, Oh, and Park.","PeriodicalId":501038,"journal":{"name":"arXiv - MATH - Representation Theory","volume":"59 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Monoidal categorification on some open Richardson varieties\",\"authors\":\"Yingjin Bi\",\"doi\":\"arxiv-2409.04715\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we investigate the cluster morphisms between cluster algebras\\nand the functor of monoidal categories. Our findings demonstrate that there\\nexists a monoidal categorification of the coordinate ring of the open\\nRichardson variety $\\\\mathcal{R}_{w,v}$, where $w=vu$ and\\n$\\\\ell(w)=\\\\ell(u)+\\\\ell(v)$. This result confirms a conjecture proposed by\\nKashiwara, Kim, Oh, and Park.\",\"PeriodicalId\":501038,\"journal\":{\"name\":\"arXiv - MATH - Representation Theory\",\"volume\":\"59 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Representation Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.04715\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Representation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.04715","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Monoidal categorification on some open Richardson varieties
In this paper, we investigate the cluster morphisms between cluster algebras
and the functor of monoidal categories. Our findings demonstrate that there
exists a monoidal categorification of the coordinate ring of the open
Richardson variety $\mathcal{R}_{w,v}$, where $w=vu$ and
$\ell(w)=\ell(u)+\ell(v)$. This result confirms a conjecture proposed by
Kashiwara, Kim, Oh, and Park.
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