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We provide a concrete relation, in terms of plethystic functions, between the generating series for <jats:italic>E<\/jats:italic>\u2010polynomials of  and the one for , generalizing a formula of Mozgovoy\u2013Reineke. The proof uses a natural stratification of  coming from affine GIT, the combinatorics of partitions, and the formula of MacDonald\u2013Cheah for symmetric products; we also adapt it to the so\u2010called Cartan brane in the moduli space of Higgs bundles. Combining our methods with arithmetic ones yields explicit expressions for the <jats:italic>E<\/jats:italic>\u2010polynomials, and Euler characteristics, of the irreducible stratum of \u2010character varieties of some groups \u0393, including surface groups, free groups, and torus knot groups, for low values of <jats:italic>n<\/jats:italic>.<\/jats:p>","DOI":"10.1002\/mana.202000416","type":"journal-article","created":{"date-parts":[[2022,10,11]],"date-time":"2022-10-11T11:56:01Z","timestamp":1665489361000},"page":"243-266","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Generating series for the <i>E<\/i>\u2010polynomials of GL(n,C)$GL(n,{\\mathbb {C}})$\u2010character varieties"],"prefix":"10.1002","volume":"296","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1001-0352","authenticated-orcid":false,"given":"Carlos","family":"Florentino","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica Faculdade de Ci\u00eancias Universidade de Lisboa Lisbon Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2331-4646","authenticated-orcid":false,"given":"Azizeh","family":"Nozad","sequence":"additional","affiliation":[{"name":"School of Mathematics Institute for Research in Fundamental Sciences (IPM) Tehran Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8340-5366","authenticated-orcid":false,"given":"Alfonso","family":"Zamora","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada a las TIC ETSI Inform\u00e1ticos Universidad Polit\u00e9cnica de Madrid Madrid Spain"}]}],"member":"311","published-online":{"date-parts":[[2022,10,11]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1112\/plms.12008"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0129167X12500826"},{"key":"e_1_2_8_4_1","first-page":"479","article-title":"On the cohomology of Hilbert schemes of points","volume":"5","author":"Cheah J.","year":"1996","journal-title":"J. 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