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We determine the mixed Hodge structure on the representation variety <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\textsf{Hom}^{0}(\\Gamma ,G)$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:msup>\n                      <mml:mi>Hom<\/mml:mi>\n                      <mml:mn>0<\/mml:mn>\n                    <\/mml:msup>\n                    <mml:mrow>\n                      <mml:mo>(<\/mml:mo>\n                      <mml:mi>\u0393<\/mml:mi>\n                      <mml:mo>,<\/mml:mo>\n                      <mml:mi>G<\/mml:mi>\n                      <mml:mo>)<\/mml:mo>\n                    <\/mml:mrow>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> and on the character variety <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\textsf{Hom}^{0}(\\Gamma ,G)\/\\!\\!\/G$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:msup>\n                      <mml:mi>Hom<\/mml:mi>\n                      <mml:mn>0<\/mml:mn>\n                    <\/mml:msup>\n                    <mml:mrow>\n                      <mml:mo>(<\/mml:mo>\n                      <mml:mi>\u0393<\/mml:mi>\n                      <mml:mo>,<\/mml:mo>\n                      <mml:mi>G<\/mml:mi>\n                      <mml:mo>)<\/mml:mo>\n                    <\/mml:mrow>\n                    <mml:mo>\/<\/mml:mo>\n                    <mml:mspace\/>\n                    <mml:mspace\/>\n                    <mml:mo>\/<\/mml:mo>\n                    <mml:mi>G<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>. We obtain explicit formulae (both closed and recursive) for the mixed Hodge polynomial of these representation and character varieties.<\/jats:p>","DOI":"10.1007\/s13163-024-00490-9","type":"journal-article","created":{"date-parts":[[2024,4,25]],"date-time":"2024-04-25T10:02:14Z","timestamp":1714039334000},"page":"121-148","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Mixed Hodge structures on character varieties of nilpotent groups"],"prefix":"10.1007","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1001-0352","authenticated-orcid":false,"given":"Carlos","family":"Florentino","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7186-3255","authenticated-orcid":false,"given":"Sean","family":"Lawton","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2468-895X","authenticated-orcid":false,"given":"Jaime","family":"Silva","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,4,25]]},"reference":[{"issue":"1","key":"490_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1017\/S0013091512000144","volume":"56","author":"A Adem","year":"2013","unstructured":"Adem, A., Cohen, F.R., G\u00f3mez, J.: Commuting elements in central products of special unitary groups. 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