1 MACDONALD INTEGRALS AND MONODROMY by Jan Denef
نویسنده
چکیده
— We prove several results on monodromies associated to Macdonald integrals, that were used in our previous work on the finite field analogue of a conjecture of Macdonald. We also give a new proof of our formula expressing recursively the zeta function of the local monodromy at the origin of the discriminant of a finite Coxeter group in terms of the degrees of the group.
منابع مشابه
Macdonald Integrals and Monodromy
We prove several results on monodromies associated to Macdonald integrals, that were used in our previous work on the finite field analogue of a conjecture of Macdonald. We also give a new proof of our formula expressing recursively the zeta function of the local monodromy at the origin of the discriminant of a finite Coxeter group in terms of the degrees of the group.
متن کاملMotivic Exponential Integrals and a Motivic Thom-sebastiani Theorem
1.1. Let f and f ′ be germs of analytic functions on smooth complex analytic varieties X and X ′ and consider the function f ⊕ f ′ on X × X ′ given by f ⊕ f (x, x) = f(x) + f (x). The Thom-Sebastiani Theorem classically states that the monodromy of f ⊕ f ′ on the nearby cycles is isomorphic to the product of the monodromy of f and the monodromy of f ′ (in the original form of the Theorem [18] t...
متن کاملMonodromy in the resonant swing spring
This paper shows that an integrable approximation of the spring pendulum, when tuned to be in 1 : 1 : 2 resonance, has monodromy. The stepwise precession angle of the swing plane of the resonant spring pendulum is shown to be a rotation number of the integrable approximation. Due to the monodromy, this rotation number is not a globally defined function of the integrals. In fact at lowest order ...
متن کاملOn a Family of Integrals that extend the Askey-Wilson Integral
We study a family of integrals parameterised by N = 2, 3, . . . generalising the Askey-Wilson integral N = 2 which has arisen in the theory of q-analogs of monodromy preserving deformations of linear differential systems and in theory of the Baxter Q operator for the XXZ open quantum spin chain. These integrals are particular examples of moments defined by weights generalising the Askey-Wilson ...
متن کاملMonodromy of A-hypergeometric functions
Using Mellin-Barnes integrals we give a method to compute a relevant subgroup of the monodromy group of an A-hypergeometric system of differential equations. Presumably this group is the full monodromy group of the system
متن کامل