Year: 2012
Type: preprint
Abstract: We prove that for every reductive group G with a maximal torus T and the Weyl group W there is a natural normalization map chi from T^N/W to an irreducible component of the G-character variety of Z^N. We prove that chi is an isomorphism for all classical groups. Additionally, we prove that even though there are no irreducible representations in the above mentioned irreducible component of the character variety for non-abelian G, the tangent spaces to it coincide with H^1(Z^N, Ad rho). Consequently, this irreducible component has the "Goldman" symplectic form for N=2, for which the combinatorial formulas for Goldman bracket hold.
Source: arXiv (Cornell University)
Author: Sikora, Adam S.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2950977869