scholarly journals Twisted strong Macdonald theorems and adjoint orbits

2016 ◽  
Vol 449 ◽  
pp. 565-614
Author(s):  
William Slofstra
Keyword(s):  
Adjoint Orbits

scholarly journals Geometric aspects of self-adjoint Sturm–Liouville problems

2017 ◽  
Vol 147 (6) ◽  
pp. 1279-1295
Author(s):  
Yicao Wang
Keyword(s):  
Boundary Conditions ◽  
Liouville Equation ◽  
Adjoint Action ◽  
Principal Type ◽  
Unitary Matrices ◽  
Adjoint Orbits ◽  
Sturm Liouville ◽  
Refined Classification ◽  
Adjoint Orbit

In this paper we use U(2), the group of 2 × 2 unitary matrices, to parametrize the space of all self-adjoint boundary conditions for a fixed Sturm–Liouville equation on the interval [0, 1]. The adjoint action of U(2) on itself naturally leads to a refined classification of self-adjoint boundary conditions – each adjoint orbit is a subclass of these boundary conditions. We give explicit parametrizations of those adjoint orbits of principal type, i.e. orbits diffeomorphic to the 2-sphere S2, and investigate the behaviour of the nth eigenvalue λnas a function on such orbits.

Paraholomorphic cohomology groups of hyperbolic adjoint orbits

2019 ◽  
Vol 43 (2) ◽  
pp. 113-143
Author(s):  
Nobutaka Boumuki ◽  
Tomonori Noda
Keyword(s):  
Cohomology Groups ◽  
Adjoint Orbits

scholarly journals ON THE EXACTNESS OF KOSTANT–KIRILLOV FORM AND THE SECOND COHOMOLOGY OF NILPOTENT ORBITS

2012 ◽  
Vol 23 (08) ◽  
pp. 1250086 ◽  
Author(s):  
INDRANIL BISWAS ◽  
PRALAY CHATTERJEE
Keyword(s):  
Lie Algebra ◽  
Lie Group ◽  
Nilpotent Orbits ◽  
Semisimple Lie Group ◽  
Simple Lie Algebra ◽  
Adjoint Orbits ◽  
Adjoint Orbit

We give a criterion for the Kostant–Kirillov form on an adjoint orbit in a real semisimple Lie group to be exact. We explicitly compute the second cohomology of all the nilpotent adjoint orbits in every complex simple Lie algebra.

scholarly journals The Complex Orthogonal Gelfand–Zeitlin System

2019 ◽  
Author(s):  
Mark Colarusso ◽  
Sam Evens
Keyword(s):  
Integrable System ◽  
Algebraic Groups ◽  
Moment Map ◽  
Linear Case ◽  
General Linear ◽  
Regular Elements ◽  
Strongly Regular ◽  
Adjoint Orbits ◽  
The Moment ◽  
Orthogonal Case

Abstract In this paper, we use the theory of algebraic groups to prove a number of new and fundamental results about the orthogonal Gelfand–Zeitlin system. We show that the moment map (orthogonal Kostant–Wallach map) is surjective and simplify criteria of Kostant and Wallach for an element to be strongly regular. We further prove the integrability of the orthogonal Gelfand–Zeitlin system on regular adjoint orbits and describe the generic flows of the integrable system. We also study the nilfibre of the moment map and show that in contrast to the general linear case it contains no strongly regular elements. This extends results of Kostant, Wallach, and Colarusso from the general linear case to the orthogonal case.

scholarly journals The structure of the space of co-adjoint orbits of a completely solvable Lie group.

1989 ◽  
Vol 36 (2) ◽  
pp. 309-320 ◽  
Author(s):  
Bradley N. Currey ◽  
Richard C. Penney
Keyword(s):  
Lie Group ◽  
Adjoint Orbits ◽  
Solvable Lie Group

scholarly journals QUATERNIONIC KAHLER MANIFOLDS OF COHOMOGENEITY ONE

1999 ◽  
Vol 10 (05) ◽  
pp. 541-570 ◽  
Author(s):  
ANDREW DANCER ◽  
ANDREW SWANN
Keyword(s):  
Simple Group ◽  
Lie Algebras ◽  
Complex Structure ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Cohomogeneity One ◽  
Cohomogeneity One Action ◽  
Hyperkähler Manifolds ◽  
Adjoint Orbits ◽  
Quaternionic Kähler

Classification results are given for (i) compact quaternionic Kähler manifolds with a cohomogeneity-one action of a semi-simple group, (ii) certain complete hyperKähler manifolds with a cohomogeneity-two action of a semi-simple group preserving each complex structure, (iii) compact 3-Sasakian manifolds which are cohomogeneity one with respect to a group of 3-Sasakian symmetries. Information is also obtained about non-compact quaternionic Kähler manifolds of cohomogeneity one and the cohomogeneity of adjoint orbits in complex semi-simple Lie algebras.

Symplectic Lefschetz fibrations on adjoint orbits

2016 ◽  
Vol 28 (5) ◽  
pp. 967-979 ◽  
Author(s):  
Elizabeth Gasparim ◽  
Lino Grama ◽  
Luiz A. B. San Martin
Keyword(s):  
Lie Algebras ◽  
Betti Numbers ◽  
Lefschetz Fibrations ◽  
Semisimple Lie Algebras ◽  
Adjoint Orbits

AbstractWe prove that adjoint orbits of semisimple Lie algebras have the structure of symplectic Lefschetz fibrations. We describe the topology of the regular and singular fibres, in particular we calculate their middle Betti numbers.

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