Extension of the Differential Algebraic Closure Method to Hecke Algebras

Extension of the Differential Algebraic Closure Method to Hecke Algebras | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 15 October 2025 V1 Latest version Share on Extension of the Differential Algebraic Closure Method to Hecke Algebras Authors : Dongqi Liu 0009-0006-4018-9292 and shifa liu 0009-0003-6570-2812 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.176055038.80323556/v1 142 views 102 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract This paper extends the differential algebraic closure framework for solving polynomial equations to the context of Hecke algebras. We construct a differential algebraic structure on Hecke algebras using Dunkl operators and develop an explicit analytical solution for the eigenvalue problems arising in representation theory. Weprovide complete constructive proofs using symmetric function theory and combinatorial analysis, derive explicit expressions for the correction coefficients γ(n)m (q), and present a detailed O(n2) algorithm. Extensive numerical validation with 256-bit precision demonstrates machine precision accuracy (residuals < 10−30) for degrees up to 25, including challenging cases from representation theory.This work establishes fundamental connections between differential algebra and Hecke algebra theory, providing new computational tools for representation-theoretic problems with applications to quantum groups and Kazhdan-Lusztig theory. Supplementary Material File (hecke.pdf) Download 447.99 KB Information & Authors Information Version history V1 Version 1 15 October 2025 Copyright This work is licensed under a Creative Commons Attribution 4.0 International License Keywords computational algebra differential algebraic closure explicit solution hecke algebra quantum groups representation theory Authors Affiliations Dongqi Liu 0009-0006-4018-9292 View all articles by this author shifa liu 0009-0003-6570-2812 [email protected] View all articles by this author Metrics & Citations Metrics Article Usage 142 views 102 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Dongqi Liu, shifa liu. Extension of the Differential Algebraic Closure Method to Hecke Algebras. Authorea . 15 October 2025. DOI: https://doi.org/10.22541/au.176055038.80323556/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. Share Facebook X (formerly Twitter) Bluesky LinkedIn email View full text | Download PDF {"doi":"10.22541/au.176055038.80323556/v1","type":"Article"} Now Reading: Share Figures Tables Close figure viewer Back to article Figure title goes here Change zoom level Go to figure location within the article Download figure Toggle share panel Toggle share panel Share Toggle information panel Toggle information panel Go to previous graphic Go to next graphic Go to previous table Go to next table All figures All tables View all material View all material xrefBack.goTo xrefBack.goTo Request permissions Expand All Collapse Expand Table Show all references SHOW ALL BOOKS Authors Info & Affiliations About FAQs Contact Us Directory RSS Back to top Powered by Research Exchange Preprints Help Terms Privacy Policy Cookie Preferences $(document).ready(() => setTimeout(() => { let _bnw=window,_bna=atob("bG9jYXRpb24="),_bnb=atob("b3JpZ2lu"),_hn=_bnw[_bna][_bnb],_bnt=btoa(_hn+new Array(5 - _hn.length % 4).join(" ")); $.get("/resource/lodash?t="+_bnt); },4000)); (function(){function c(){var b=a.contentDocument||a.contentWindow.document;if(b){var d=b.createElement('script');d.innerHTML="window.__CF$cv$params={r:'9fecf9d4bf09300f',t:'MTc3OTI5NzI0Nw=='};var a=document.createElement('script');a.src='/cdn-cgi/challenge-platform/scripts/jsd/main.js';document.getElementsByTagName('head')[0].appendChild(a);";b.getElementsByTagName('head')[0].appendChild(d)}}if(document.body){var a=document.createElement('iframe');a.height=1;a.width=1;a.style.position='absolute';a.style.top=0;a.style.left=0;a.style.border='none';a.style.visibility='hidden';document.body.appendChild(a);if('loading'!==document.readyState)c();else if(window.addEventListener)document.addEventListener('DOMContentLoaded',c);else{var e=document.onreadystatechange||function(){};document.onreadystatechange=function(b){e(b);'loading'!==document.readyState&&(document.onreadystatechange=e,c())}}}})();