2018
DOI: 10.1515/jgth-2018-0120
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Poincaré series of character varieties for nilpotent groups

Abstract: For any compact and connected Lie group G and any free abelian or free nilpotent group Γ , we determine the cohomology of the path component of the trivial representation of the representation space (character variety) Rep(Γ, G) 1 , with coefficients in a field F with char(F) either 0 or relatively prime to the order of the Weyl group W . We give explicit formulas for the Poincaré series. In addition we study G-equivariant stable decompositions of subspaces X(q, G) of the free monoid J(G) generated by the Lie … Show more

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Cited by 7 publications
(1 citation statement)
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“…The authors [50] gave an explicit formula for the Poincaré series of the path component of the trivial representation Hom(Z n , G) 1 using methods from [20], and the second author [56] gave a similar formula for the path component Rep(Z n , G) 1 :…”
mentioning
confidence: 99%
“…The authors [50] gave an explicit formula for the Poincaré series of the path component of the trivial representation Hom(Z n , G) 1 using methods from [20], and the second author [56] gave a similar formula for the path component Rep(Z n , G) 1 :…”
mentioning
confidence: 99%