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arXiv · 1705.01443

Poincare series of character varieties for nilpotent groups

Mentor Stafa
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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 group $G$, obtained from finitely generated free nilpotent group representations.

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Mentor Stafa. 2017-05-03. Poincare series of character varieties for nilpotent groups. https://doi.org/10.1515/jgth-2018-0120

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