# Lie groups, Nahm's equations and hyperkaehler manifolds

@article{Bielawski2005LieGN, title={Lie groups, Nahm's equations and hyperkaehler manifolds}, author={Roger Bielawski}, journal={arXiv: Differential Geometry}, year={2005} }

Lectures given at the summer school on Algebraic Groups, Goettingen, June 27 - July 15 2005

## 14 Citations

INFORMAL NOTES ON HYPERKÄHLER GEOMETRY

- Mathematics
- 2012

Informal notes prepared for the CAMGSD working seminar on Symplectic/Contact Geometry/Topology.

On 2d TQFTs whose values are holomorphic symplectic varieties

- Mathematics
- 2011

For simple and simply-connected complex algebraic group G, we conjecture the existence of a functor eta_G from the category of 2-bordisms to the category of holomorphic symplectic varieties with…

A hyperholomorphic line bundle on certain hyperkähler manifolds not admitting an S1-symmetry

- Mathematics
- 2015

Parabolic Higgs bundles and representations of the fundamental group of a punctured surface into a real group

- MathematicsAdvances in Mathematics
- 2020

On 6d N = (2, 0) theory compactified on a Riemann surface with finite area

- MathematicsProgress of Theoretical and Experimental Physics
- 2013

We study 6d N=(2,0) theory of type SU(N) compactified on Riemann surfaces with finite area, including spheres with fewer than three punctures. The Higgs branch, whose metric is inversely proportional…

S-duality of boundary conditions in N=4 super Yang-Mills theory

- Physics
- 2008

By analyzing brane configurations in detail, and extracting general lessons, we develop methods for analyzing S-duality of supersymmetric boundary conditions in N=4 super Yang-Mills theory. In the…

Supersymmetric Boundary Conditions in
$\mathcal{N}=4$
Super Yang-Mills Theory

- Mathematics
- 2008

AbstractWe study boundary conditions in
${\mathcal{N}}=4$
super Yang-Mills theory that preserve one-half the supersymmetry. The obvious Dirichlet boundary conditions can be modified to allow some…

Boundaries and Defects of N = 4 SYM with 4 Supercharges Part II : Brane Constructions and 3 d N = 2 Field Theories

- Physics
- 2014

We study the vacuum moduli spaces of 3d N = 2 supersymmetric quantum field theories by applying the formalism developed in our previous paper [1]. The 3d theories can be realized by branes in type…

2 2 M ay 2 01 8 Skyrme model from 6 d N = ( 2 , 0 ) theory

- Mathematics
- 2018

We consider 5d Yang–Mills theory with a compact ADE-type gauge group G on R × I, where I is an interval. The maximally supersymmetric extension of this model appears after compactification on S of 6d…

## References

SHOWING 1-10 OF 120 REFERENCES

Group cohomology and the singularities of the Selberg zeta function associated to a Kleinian group

- Mathematics
- 1996

We prove Patterson's conjecture about the singularities of the Selberg zeta function associated to a convex-cocompact, torsion free group acting on a hyperbolic space.

Algebraic Geometry

- MathematicsNature
- 1973

Introduction to Algebraic Geometry.By Serge Lang. Pp. xi + 260. (Addison–Wesley: Reading, Massachusetts, 1972.)

Algebraic loop groups and moduli spaces of bundles

- Mathematics
- 2003

Abstract.We study algebraic loop groups and affine Grassmannians in positive characteristic. The main results are normality of Schubert-varieties, the construction of line-bundles on the affine…

GENERALIZED BESSEL MODELS FOR A SYMPLECTIC GROUP OF RANK 2

- Mathematics
- 1973

In this paper we prove a uniqueness theorem for an analogue of the Bessel model of an irreducible representation of a symplectic group of rank 2 over a disconnected local field. Bibliography: 4 items.

Fuchsian groups of the second kind and representations carried by the limit set

- Mathematics
- 1997

Fuchsian groups of the second kind and representations carried by the limit set Dedicated to Rolf Sulanke on the occasion of his 65'th birthday.

Nahm's equations and the classification of monopoles

- Mathematics
- 1984

Solutions of Nahm's system of ordinary differential equations are produced by variational methods. This leads to an explicit parametrisation of the solutions to the Bogomolny equation over ℝ3.

Quasi-Equivariant D -Modules, Equivariant Derived Category, and Representations of Reductive Lie Groups

- Mathematics
- 1994

In this note, we describe proofs of certain conjectures on functorial, geometric constructions of representations of a reductive Lie group G R . Our methods have applications beyond the conjectures…

The 2-adic Eigencurve is Proper

- Computer Science
- 2005

The question whether the Eigencurve has any "holes" is answered in the negative for the 2-adic EigenCurve of tame level one.

Cohomological Properties of the Canonical Globalizations of Harish–Chandra Modules

- Mathematics
- 1996

In this note we draw consequences of theorems of Kashiwara–Schmid, Casselman, and Schneider–Stuhler. Canonical globalizations of Harish–Chandra modules can be considered as coefficient modules for…

The Burger-Sarnak method and operations on the unitary dual of ()

- Mathematics
- 2005

We study the effect of restriction to Levi subgroups, induction from Levi subgroups, and tensor product, on unitary representations of GL(n) over a local field k. These results give partial answers…