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CASIMIR OPERATORS AND MONODROMY REPRESENTATIONS OF GENERALISED BRAID GROUPS
CASIMIR OPERATORS MONODROMY REPRESENTATIONS GENERALISED BRAID GROUPS
2015/10/14
Let g be a complex, simple Lie algebra with Cartan subalgebra h and Weyl group W . We construct a one parameter family of flat connections ∇κ on h with values in any finite–dimensional g–moduleV...
Abstract: We show that the monodromy operator action on the first cohomology group of the Milnor fiber is combinatorially determined for line arrangements with at most triple points and containing at ...
Tate properties, polynomial-count varieties, and monodromy of hyperplane arrangements
hyperplane arrangement Milnor fiber monodromy polynomial-count
2011/1/19
A necessary and sufficient condition for the triviality of the Milnor monodromy of a central hyperplane arrangement is given. This is a consequence of a Thom-Sebastiani type result, where the sum of h...
A Kohno-Drinfeld theorem for the monodromy of cyclotomic KZ connections
Kohno-Drinfeld theorem cyclotomic KZ connections
2010/11/23
We compute explicitly the monodromy representations of "cyclotomic" analogs of the Knizhnik--Zamolodchikov differential system. These are representations of the type B braid group $B_n^1$. We show ho...
Higher order Painleve system of type D^{(1)}_{2n+2} and monodromy preserving deformation
Painleve system monodromy preserving deformation
2010/11/8
The higher order Painleve system of type D^{(1)}_{2n+2} is proposed by Y. Sasano. It is an extension of the sixth Painleve equation for the affine Weyl group symmetry and expressed as a Hamiltonian sy...
We prove a strong form of the motivic monodromy conjecture for abelian varieties, by showing that the order of the unique pole of the motivic zeta function is equal to the size of the maximal Jordan b...
Gravitational Solitons and Monodromy Transform Approach to Solution of Integrable Reductions of Einstein Equations
Gravitational Solitons Monodromy Transform Solution
2010/11/2
In this paper the well known Belinskii and Zakharov soliton generating transformations of the solution space of vacuum Einstein equations with two-dimensional Abelian groups of isometries are consider...
The monodromy groupoid was first inlioduced by Pradines in [7] and developed by Mucuk in [6] In this paper we give an application of the monodromy groupoid.