{"title":"变性环状赫克布拉上的马尔可夫迹线","authors":"Deke Zhao","doi":"arxiv-2409.09372","DOIUrl":null,"url":null,"abstract":"Let $H_n(\\boldsymbol{u})$ be the degenerate cyclotomic Hecke algebra with\nparameter $\\boldsymbol{u}=(u_1, \\ldots, u_m)$ over\n$\\mathbb{C}(\\boldsymbol{u})$. We define and construct the (non-)normalized\nMarkov traces on the sequence $\\{H_n(\\boldsymbol{u})\\}_{n=1}^{\\infty}$. This\nallows us to provide a canonical symmetrizing form on $H_n(\\boldsymbol{u})$ and\nshow that the Brudan--Kleshchev trace on $H_n(\\boldsymbol{u})$ is a\nspecialization of the non-normalized Markov traces.","PeriodicalId":501136,"journal":{"name":"arXiv - MATH - Rings and Algebras","volume":"31 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Markov traces on degenerate cyclotomic Hecke algebras\",\"authors\":\"Deke Zhao\",\"doi\":\"arxiv-2409.09372\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $H_n(\\\\boldsymbol{u})$ be the degenerate cyclotomic Hecke algebra with\\nparameter $\\\\boldsymbol{u}=(u_1, \\\\ldots, u_m)$ over\\n$\\\\mathbb{C}(\\\\boldsymbol{u})$. We define and construct the (non-)normalized\\nMarkov traces on the sequence $\\\\{H_n(\\\\boldsymbol{u})\\\\}_{n=1}^{\\\\infty}$. This\\nallows us to provide a canonical symmetrizing form on $H_n(\\\\boldsymbol{u})$ and\\nshow that the Brudan--Kleshchev trace on $H_n(\\\\boldsymbol{u})$ is a\\nspecialization of the non-normalized Markov traces.\",\"PeriodicalId\":501136,\"journal\":{\"name\":\"arXiv - MATH - Rings and Algebras\",\"volume\":\"31 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Rings and Algebras\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.09372\",\"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 - Rings and Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09372","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Markov traces on degenerate cyclotomic Hecke algebras
Let $H_n(\boldsymbol{u})$ be the degenerate cyclotomic Hecke algebra with
parameter $\boldsymbol{u}=(u_1, \ldots, u_m)$ over
$\mathbb{C}(\boldsymbol{u})$. We define and construct the (non-)normalized
Markov traces on the sequence $\{H_n(\boldsymbol{u})\}_{n=1}^{\infty}$. This
allows us to provide a canonical symmetrizing form on $H_n(\boldsymbol{u})$ and
show that the Brudan--Kleshchev trace on $H_n(\boldsymbol{u})$ is a
specialization of the non-normalized Markov traces.