monodromy sentence in Hindi
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- The equivalence between the two definitions of Hurwitz numbers ( counting ramified coverings of the sphere, or counting transitive factorizations ) is established by describing a ramified covering by its monodromy.
- In that case the monodromy group relating solutions by analytic continuation has less to say in general, and the solutions are harder to study, except in terms of their asymptotic expansions.
- The monodromy theorem makes it possible to extend an analytic function to a larger set via curves connecting a point in the original domain of the function to points in the larger set.
- Note that the monodromy defects discussed above are not finite-energy excitations in the spectrum of the Hamiltonian, but defects created by "'modifying "'the Hamiltonian.
- Here the branch point is the origin, because the analytic continuation of any solution around a closed loop containing the origin will result in a different function : there is non-trivial monodromy.
- The monodromy describes the way the first homology group of a smooth fiber ( which is isomorphic to "'Z "'2 ) changes as we go around a singular fiber.
- The action on V _ 1 \ otimes \ dots \ otimes V _ n by the analytic continuation of KZ equation is called "'monodromy representation of KZ equation " '.
- There he considered the problem of isomonodromy deformations for a certain matrix Fuchsian equation; this is a special case of Hilbert's 21st Problem ( existence of differential equations with prescribed monodromy ).
- It is known that the monodromy representation of KZ equation with a general semi-simple Lie algebra agrees with the linear representation of braid group given by R-matrix of the corresponding quantum group.
- The monodromy around each singular fiber is a well-defined conjugacy class in the group SL ( 2, "'Z "') of 2 ?2 integer matrices with determinant 1.
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