{"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}
引用次数: 0
Abstract
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.