Poincaré series of character varieties for nilpotent groups-Reference-Cited by-同舟云学术

Poincaré series of character varieties for nilpotent groups

Published:2018-12-18 Issue:3 Volume:22 Page:419-440
ISSN:1435-4446
Container-title:Journal of Group Theory
language:en
Short-container-title:

Author:

Stafa Mentor¹

Affiliation:

1. Department of Mathematics , Tulane University , New Orleans , LA 70118 , USA

Abstract

Abstract For any compact, connected Lie group G and any finitely generated nilpotent group Γ, we determine the cohomology of the path component of the trivial representation of the group character variety (representation space) Rep ⁢ ( Γ , G ) 1

{{\rm Rep}(\Gamma,G)_{1}}

, with coefficients in a field 𝔽

{{\mathbb{F}}}

with characteristic 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 )

{{\rm X}(q,G)}

of the free monoid J ⁢ ( G )

{J(G)}

generated by the Lie group G, obtained from representations of finitely generated free nilpotent groups.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

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