19 citations · 45 across the 14 of their papers we have counts for
17 papers
Skein modules of closed 3 manifolds define line bundles over character varieties
Julien Korinman
Let M be a closed 3-manifold and S(M) the skein module of M at some odd root of unity. Using the Frobenius morphism, we can see S(M) as the space of global sections of a coherent s…
A survey on mapping class group representations derived from skein theory
Julien Korinman
We survey various constructions of finite dimensional projective representations of mapping class groups derived from stated skein algebras.
Classification of semi-weight representations of reduced stated skein algebras
H. Karuo, J. Korinman
We classify the finite dimensional semi-weight representations of the reduced stated skein algebras at odd roots of unity of connected marked surfaces which either have a boundary…
Relating quantum character varieties and skein modules
Julien Korinman, Jun Murakami
We relate the Kauffman bracket stated skein modules to two independent constructions of quantum representation spaces of Habiro and Van der Veen with the second author. We deduce f…
Azumaya loci of skein algebras
Hiroaki Karuo, Julien Korinman
We compute the Azumaya loci of Kauffman-bracket skein algebras of closed surfaces at odd roots of unity and provide partial results for open surfaces as well. As applications, we g…
Mapping Class Group Representations Derived from Stated Skein Algebras
Julien Korinman
We construct finite-dimensional projective representations of the mapping class groups of compact connected oriented surfaces having one boundary component using stated skein algeb…
Stated skein algebras and their representations
Julien Korinman
This is a survey on stated skein algebras and their representations.
Finite presentations for stated skein algebras and lattice gauge field theory
Julien Korinman
We provide finite presentations for stated skein algebras and deduce that those algebras are Koszul and that they are isomorphic to the quantum moduli algebras appearing in lattice…
Unicity for representations of reduced stated skein algebras
Julien Korinman
We prove that both stated skein algebras and their reduced versions at odd roots of unity are almost-Azumaya and compute the rank of a reduced stated skein algebra over its center,…
Quantum holonomic link invariants derived from stated skein algebras
Julien Korinman
We define invariants for a framed link equipped with a SL2 local system in its complement and additional combinatorial data based on the theory of representations of stated skein a…
The quantum trace as a quantum non-abelianization map
Julien Korinman, Alexandre Quesney
We prove that the balanced Chekhov-Fock algebra of a punctured triangulated surface is isomorphic to a skein algebra which is a deformation of the algebra of regular functions of s…
Classical shadows of stated skein representations at roots of unity
Julien Korinman, Alexandre Quesney
We extend some results of Bonahon, Bullock, Turaev and Wong concerning the skein algebras of closed surfaces to L^e's stated skein algebra associated to open surfaces. We prove tha…
Triangular decomposition of character varieties
Julien Korinman
A marked surface is a compact oriented surface equipped with some pairwise disjoint arcs embedded in its boundary. In this paper, we extend the notion of character varieties to mar…
A quantum ergodic theorem for mapping class groups action on character variety
Julien Korinman
We state a theorem relating the ergodicity of the action of a given subgroup of the mapping class group of a surface on the character variety, to the asymptotic of its invariant su…
On the (in)finiteness of the image of Reshetikhin-Turaev representations
Julien Korinman
We state a simple criterion to prove the infiniteness of the image of Reshetikhin-Turaev irreducible representations of the mapping class groups of surfaces. We use it to study som…
Decomposition of some Witten-Reshetikhin-Turaev Representations into Irreducible Factors
Julien Korinman
We decompose into irreducible factors the Witten-Reshetikhin-Turaev representations of the mapping class group of a genus surface when the level is and $p=…
Irreducible factors of Weil representations and TQFT
Julien Korinman
We give the decomposition into irreducible factors of Weil representations of the symplectic groups at even levels, generalizing previous decompositions at odd levels. We then deri…