220 citations · 410 across the 11 of their papers we have counts for
12 papers
Topological quantum field theories from Hecke algebras
Vladimir Fock, Valdo Tatitscheff, Alexander Thomas
We construct two-dimensional non-commutative topological quantum field theories (TQFTs), one for each Hecke algebra corresponding to a finite Coxeter system. These TQFTs associate…
Riemann geometry without indices
Vladimir V. Fock, Pierre Goussard
We suggest an index-free formalism allowing to simplify many computations in Riemann geometry. The main ingredients are forms with values in a Clifford algebra and an action of the…
Symplectic double for moduli spaces of G-local systems on surfaces
Vladimir Fock, Alexander Goncharov
Let G be a split semi-simple algebraic group over Q. Let S be a decorated surface, that is a topological oriented surface with a finite set of marked points on the boundary, consid…
Cluster X-varieties at infinity
V. V. Fock, A. B. Goncharov
A positive space is a space with a positive atlas, i.e. a collection of rational coordinate systems with subtraction free transition functions. The set of positive real points of a…
Cluster ensembles, quantization and the dilogarithm II: The intertwiner
V. V. Fock, A. B. Goncharov
The main result is a construction, via the quantum dilogarithm, of certain intertwiner operators, which play the crucial role in the quantization of the cluster X-varieties and con…
The quantum dilogarithm and representations quantum cluster varieties
V. V. Fock, A. B. Goncharov
We construct, using the quantum dilogarithm, a series of *-representations of quantized cluster varieties. This includes a construction of infinite dimensional unitary projective r…