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Daisuke Yamakawa

Publications and source records attributed to Daisuke Yamakawa.

12 recordsLinked to original sources
arXiv2026

Wild genus-zero quantum de Rham spaces

The wild de Rham spaces parameterize isomorphism classes of (stable) meromorphic connections, defined on principal bundles over wild Riemann surfaces. Working on the Riemann sphere, we will deformation-quantize the standard open part of de Rham spaces, which corresponds to the moduli of linear ordinary differential equations with meromorphic coefficients. We treat the general untwisted/unramified case with nonresonant semisimple formal residue, for any polar divisor and reductive structure group. The main ingredients are: (i) constructing the quantum Hamiltonian reduction of a (tensor) product of quantized coadjoint orbits in dual truncated-current Lie algebras, involving the corresponding category-O Verma modules; and (ii) establishing sufficient conditions on the coadjoint orbits, so that generically all meromorphic connections are stable, and the (semiclassical) moment map for the gauge-group action is faithfully flat.

math.QA↗
arXiv2025

Polystability of Stokes representations and differential Galois groups

Polystability of (twisted) Stokes representations (i.e. wild monodromy representations) will be characterised, in terms of the corresponding differential Galois group (generalising the Zariski closure of the monodromy group in the tame case). This extends some results of Richardson. Further, the intrinsic approach to such results will be established, in terms of reductions of Stokes local systems.

math.AG↗
arXiv2025

Twisted local G-wild mapping class groups

We consider the isomonodromic deformations of irregular-singular connections defined on principal bundles over complex curves: for any complex reductive structure group G, and any polar divisor; allowing for a twisted/ramified formal normal form at each pole, and for twists in the interior of the curve. (This covers the general case in 2-dimensional meromorphic gauge theory.) We focus on the irregular moduli of the connections, studying the fundamental groups of the spaces of admissible deformations of their irregular types/classes, i.e., the local wild mapping class groups in the title. To describe them, we first take the viewpoint of (nonsplit) reflections cosets in Springer/Lehrer--Springer theory, which yields in particular new modular interpretations of complex reflection groups -- and their braid groups. Then we introduce new `fission' trees to treat structure groups of any (simple) classical type, leading to a complete classification of the corresponding hyperplane arrangements, and singling out an infinite family of noncrystallographic examples in type D. Moreover, we reinterpret Bessis' lift of Springer theory as the study of `quasi-generic' deformations, corresponding to irregular singularities whose leading coefficient is regular semisimple upon pullback along a local cyclic covering of the base curve. Finally, we rephrase much of this material in terms of generalized root-valuation stratifications.

math.GT↗
arXiv2025

Unfolding of wild character varieties

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 into regular ones. Furthermore, we show that these unfolding Poisson maps induce Poisson birational equivalences between wild and tame character varieties. This result provides an affirmative answer to a conjecture posed by Klimes, Paul, and Ramis.

math.AG↗
arXiv2025

Symmetries of Quiver Schemes

We introduce reflection functors on quiver schemes in the sense of Hausel--Wong--Wyss, generalizing those on quiver varieties. Also we construct some isomorphisms between quiver schemes whose underlying quivers are different.

math.AG↗
arXiv2014

Fourier-Laplace transform and isomonodromic deformations

Using the Fourier-Laplace transform, we describe the isomonodromy equations for meromorphic connections on the Riemann sphere with unramified irregular singularities as those for connections with a (possibly ramified) irregular singularity and a regular singularity. This generalizes some results of Harnad and Woodhouse.

math.CA↗
arXiv2014

Moduli spaces of meromorphic connections and quiver varieties

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 arbitrary number of simple poles as Nakajima's quiver varieties. This result enables us to solve partially the additive irregular Deligne-Simpson problem.

math.DG↗
arXiv2010

Quiver Varieties with Multiplicities, Weyl Groups of Non-Symmetric Kac-Moody Algebras, and Painlevé Equations

To a finite quiver equipped with a positive integer on each of its vertices, we associate a holomorphic symplectic manifold having some parameters. This coincides with Nakajima's quiver variety with no stability parameter/framing if the integers attached on the vertices are all equal to one. The construction of reflection functors for quiver varieties are generalized to our case, in which these relate to simple reflections in the Weyl group of some symmetrizable, possibly non-symmetric Kac-Moody algebra. The moduli spaces of meromorphic connections on the rank 2 trivial bundle over the Riemann sphere are described as our manifolds. In our picture, the list of Dynkin diagrams for Painlevé equations is slightly different from (but equivalent to) Okamoto's.

math.RT↗
arXiv2010

Middle Convolution and Harnad Duality

We interpret the additive middle convolution operation in terms of the Harnad duality, and as an application, generalize the operation to have a multi-parameter and act on irregular singular systems.

math.CA↗
arXiv2007

Geometry of Multiplicative Preprojective Algebra

Crawley-Boevey and Shaw recently introduced a certain multiplicative analogue of the deformed preprojective algebra, which they called the multiplicative preprojective algebra. In this paper we study the moduli space of (semi)stable representations of such an algebra (the multiplicative quiver variety), which in fact has many similarities to the quiver variety. We show that there exists a complex analytic isomorphism between the nilpotent subvariety of the quiver variety and that of the multiplicative quiver variety (which can be extended to a symplectomorphism between these tubular neighborhoods). We also show that when the quiver is star-shaped, the multiplicative quiver variety parametrizes Simpson's (poly)stable filtered local systems on a punctured Riemann sphere with prescribed filtration type, weight and associated graded local system around each puncture.

math.SG↗