Results 1  10
of
301
with Fuchsian and irregular singularities
, 2011
"... q−asymptotics for linear q−differencedifferential equations ..."
Asymptotics at irregular singular points
"... 1. Example: rotationally symmetric eigenfunctions on Rn 2. Example: translationequivariant eigenfunctions on H 3. Beginning of construction of solutions 4. K(x, t) is bounded ..."
Abstract
 Add to MetaCart
1. Example: rotationally symmetric eigenfunctions on Rn 2. Example: translationequivariant eigenfunctions on H 3. Beginning of construction of solutions 4. K(x, t) is bounded
Harmonic metrics and connections with irregular singularities
 Ann. Inst. Fourier (Grenoble
, 1999
"... Abstract. We identify the holomorphic de Rham complex of the minimal extension of a meromorphic vector bundle with connexion on a compact Riemann surface X with the L 2 complex relative to a suitable metric on the bundle and a complete metric on the punctured Riemann surface. Applying results of C. ..."
Abstract

Cited by 12 (2 self)
 Add to MetaCart
, equipped with a connection ∇ : M → M ⊗OX Ω1 X = X − D ֒ → X. Let M be a locally free OX[∗D]module of finite rank which may have regular or irregular singularities at each point of D. Therefore, M is also a holonomic module on the ring DX of holomorphic differential operators on X. We call such a DX
Periods for irregular singular connections on surfaces
"... Abstract: Given an integrable connection on a smooth quasiprojective algebraic surface U over a subfield k of the complex numbers, we define rapid decay homology groups with respect to the associated analytic connection which pair with the algebraic de Rham cohomology in terms of period integrals. ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
Abstract: Given an integrable connection on a smooth quasiprojective algebraic surface U over a subfield k of the complex numbers, we define rapid decay homology groups with respect to the associated analytic connection which pair with the algebraic de Rham cohomology in terms of period integrals. These homology groups generalize the analogous groups in the same situation over curves defined by S. Bloch and H. Esnault. In dimension two, however, new features appear in this context which we explain in detail. Assuming a conjecture of C. Sabbah on the formal classification of meromorphic connections on surfaces (known to be true if the rank is lower than or equal to 5), we prove perfectness of the period pairing in dimension two. 1
Solving in the Neighbourhood of an Irregular Singular Point
"... This study expresses the solution of the Bessel equation in the neighbourhood of = ∞ as the product of a knownform singular divisor and a specific nonsingular function, which satisfies the corresponding derived equation. Considering the failure of the traditional irregular solution constructed wit ..."
Abstract
 Add to MetaCart
This study expresses the solution of the Bessel equation in the neighbourhood of = ∞ as the product of a knownform singular divisor and a specific nonsingular function, which satisfies the corresponding derived equation. Considering the failure of the traditional irregular solution constructed
ToledanoLaredo V., Gaudin model with irregular singularities
"... Abstract. We introduce a class of quantum integrable systems generalizing the Gaudin model. The corresponding algebras of quantum Hamiltonians are obtained as quotients of the center of the enveloping algebra of an affine Kac–Moody algebra at the critical level, extending the construction of higher ..."
Abstract

Cited by 24 (3 self)
 Add to MetaCart
Gaudin Hamiltonians from [FFR] to the case of nonhighest weight representations of affine algebras. We show that these algebras are isomorphic to algebras of functions on the spaces of opers on P 1 with regular as well as irregular singularities at finitely many points. We construct eigenvectors
Opers with irregular singularity and spectra of the shift of argument subalgebra
, 2007
"... The universal enveloping algebra of any simple Lie algebra g contains a family of commutative subalgebras, called the quantum shift of argument subalgebras [R, FFT]. We prove that generically their action on finitedimensional modules is diagonalizable and their joint spectra are in bijection with ..."
Abstract

Cited by 13 (2 self)
 Add to MetaCart
with the set of monodromyfree L Gopers on P¹ with regular singularity at one point and irregular singularity of order two at another point. We also prove a multipoint generalization of this result, describing the spectra of commuting Hamiltonians in Gaudin models with irregular singulairity. In addition, we
On the generalized RiemannHilbert problem with irregular singularities
 Expo. Math
"... In this article we study the generalized RiemannHilbert problem, which extends the classical RiemannHilbert problem to the case of irregular singularities. The problem is stated in terms of generalized monodromy data which include the monodromy representation, Stokes matrices and the true Poincaré ..."
Abstract

Cited by 11 (2 self)
 Add to MetaCart
In this article we study the generalized RiemannHilbert problem, which extends the classical RiemannHilbert problem to the case of irregular singularities. The problem is stated in terms of generalized monodromy data which include the monodromy representation, Stokes matrices and the true
Results 1  10
of
301