Generators, relations and symmetries in pairs of 3×3 unimodular matrices
By Sean Lawton. 2006
67 citations recorded by the source corpus.
Abstract Denote the free group on two letters by F 2 and the SL ( 3 , C ) -representation variety of F 2 by R = Hom ( F 2 , SL ( 3 , C ) ) . There is a SL ( 3 , C ) -action on the coordinate ring of R , and the geometric points of the subring of invariants is an affine variety X . We determine explicit minimal generators and defining relations for the subring of invariants and show X is a degree 6 hyper-surface in C 9 mapping onto C 8 . Our choice of generators exhibit Out ( F 2 ) symmetries which allow for a succinct expression of the defining relations.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/584200db9b785352a2eba4299ec0b824cf9beee5
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- The topology of moduli spaces of free group representations (2008, methodology): “ generators. It generates the ideal. (iv) This relation is of the form t2 − Pt+Qwhere P= tr(X1X2X −1 1 X −1 2 )+tr(X2X1X −1 2 X −1 1 ) and Q= tr(X1X2X −1 1 X −1 2 )tr(X2X1X −1 2 X −1 1 ) We note that [Law07] provides explicit formulas for Pand Qin terms of the first eight elements of G. Said different”