16 citations · 26 across the 14 of their papers we have counts for
14 papers
Middle convolution for Lie algebra representations
Kazuki Hiroe
This paper introduces a Lie algebra analogue of the middle convolution functor, which is defined on the category of modules over certain Lie algebras, including, as typical motivat…
Middle convolution for affine hyperplane arrangements and Aomoto realizability
Shunya Adachi, Kazuki Hiroe
We construct middle convolution for local systems on complements of affine hyperplane arrangements. Our aim is to study Aomoto realizability: whether a local system can be realized…
Unfolding of wild character varieties
Kazuki Hiroe, Daisuke Yamakawa
In this paper, we study wild character varieties on compact Riemann surfaces and construct Poisson maps from wild to tame character varieties by unfolding irregular singularities i…
Deformation of moduli spaces of meromorphic -connections on via unfolding of irregular singularities
Kazuki Hiroe
Unfolding singular points in linear differential equations is a classical technique for studying the properties of irregular singularities by relating them to regular singularities…
Long-Moody construction of braid representations and Katz middle convolution
Kazuki Hiroe, Haru Negami
The Long-Moody construction is a method to obtain representations of braid groups introduced by Long and Moody. Also the Katz middle convolution is known to be a method to construc…
A note on unfolding manifolds of meromorphic connections on the Riemann sphere with unramified singularities
Kazuki Hiroe
This note explains a construction of a Poisson manifold whose symplectic foliation describes a deformation of a moduli space of meromorphic connections with unramified irregular si…
Index of rigidity of differential equations and Euler characteristic of their spectral curves
Kazuki Hiroe
We show a coincidence of index of rigidity of differential equations with irregular singularities on a compact Riemann surface and Euler characteristic of the associated spectral c…
Moduli spaces of meromorphic connections, quiver varieties, and integrable deformations
Kazuki Hiroe
This is a note in which we first review symmetries of moduli spaces of stable meromorphic connections on trivial vector bundles over the Riemann sphere, and next discuss symmetries…
Local Fourier transform and blowing up
Kazuki Hiroe
We consider a resolution of ramified irregular singularities of meromorphic connections on a formal disk via local Fourier transforms. A necessary and sufficient condition for an i…
Linear differential equations on the Riemann sphere and representations of quivers
Kazuki Hiroe
Our interest in this paper is a generalization of the additive Deligne-Simpson problem which is originally defined for Fuchsian differential equations on the Riemann sphere. We sha…
Moduli spaces of meromorphic connections and quiver varieties
Kazuki Hiroe, Daisuke Yamakawa
We describe the moduli spaces of meromorphic connections on trivial holomorphic vector bundles over the Riemann sphere with at most one (unramified) irregular singularity and arbit…
Linear differential equations on and root systems
Kazuki Hiroe
In this paper, we study the Euler transform on linear ordinary differential operators on . The spectral type is the tuple of integers which count the multiplicities…
Twisted Euler transform of differential equations with an irregular singular point
Kazuki Hiroe
N. Katz introduced the notion of the middle convolution on local systems. This can be seen as a generalization of the Euler transform of Fuchsian differential equations. In this pa…
Generalized Whittaker functions for degenerate principal series of
Kazuki Hiroe
We give a characterization of a generalized Whittaker model of a degenerate principal series representation of as the kernel of some differential operators. By this char…