A. A. Florentino, CarlosLawton, SeanSilva, Jaime2024-11-112024-11-112024-04Florentino C, Lawton S, Silva J. Mixed Hodge structures on character varieties of nilpotent groups. Revista Matemática Complutense. 2024; 9. https://doi.org/10.1007/s13163-024-00490-91139-1138http://hdl.handle.net/10400.21/17872Let Hom0(Ƭ, G) be the connected component of the identity of the variety of representations of a finitely generated nilpotent group into a connected reductive complex affine algebraic group G. We determine the mixed Hodge structure on the representation variety Hom0(Ƭ, G) and on the character variety Hom0(Ƭ, G)//G. We obtain explicit formulae (both closed and recursive) for the mixed Hodge polynomial of these representation and character varieties.engcharacter varietymixed Hodge structuresnilpotent groupHodge polynomialjournal article10.1007/s13163-024-00490-91988-2807