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Advances in Mathematics, ISSN 0001-8708, 01/2017, Volume 305, pp. 1 - 77
According to a theorem of Brieskorn and Slodowy, the intersection of the nilpotent cone of a simple Lie algebra with a transverse slice to the subregular nilpotent orbit is a simple surface singularity... 
Symplectic singularities | Nilpotent orbits | Slodowy slice | LIE-ALGEBRAS | MATHEMATICS | UNIPOTENT CLASSES | GREEN-FUNCTIONS | REPRESENTATIONS | VARIETIES | CHEVALLEY-GROUPS | CONTRACTIONS | Algebra
Journal Article
International Journal of Modern Physics A, ISSN 0217-751X, 02/2013, Volume 28, Issue 3-4
... = A, D, E labeled by nilpotent orbits of a Lie algebra g, where g is determined by J and the outer-automorphism twist around the defect... 
defect operators | nilpotent orbits | Superconformal field theory | ALGEBRAS | PHYSICS, NUCLEAR | COVERS | SELF-DUAL STRINGS | SHEETS | PHYSICS, PARTICLES & FIELDS
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 01/2019, Volume 371, Issue 1, pp. 105 - 136
Journal Article
Journal of Algebra, ISSN 0021-8693, 10/2017, Volume 487, pp. 317 - 339
In this manuscript, we compute explicitly the Lusztig–Vogan bijection for local systems of some classical, special, nilpotent orbits... 
Unipotent representations | Quantization | Nilpotent orbits | Orbit method | MATHEMATICS | REGULAR FUNCTIONS
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 12/2018, Volume 275, Issue 12, pp. 3338 - 3379
Let G be a connected, simply connected nilpotent group and π be an irreducible unitary representation of G that is square-integrable modulo its center Z(G) on... 
Parametrization of coadjoint orbits | Square-integrable representation | Uniform subgroup | Nilpotent Lie group | DENSITY | MATHEMATICS | FRAMES | ATOMIC DECOMPOSITIONS | SPACES | PSEUDODIFFERENTIAL-OPERATORS
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 06/2018, Volume 546, pp. 210 - 260
The Jordan type of a nilpotent matrix is the partition giving the sizes of its Jordan blocks. We study pairs of partitions (P,Q), where Q=Q(P) is the Jordan... 
Generic commuting orbit | Partition | Nilpotent orbit | Jordan type | Commuting nilpotent matrices | MATHEMATICS, APPLIED | VARIETIES | CENTRALIZERS | MATHEMATICS | ELEMENTS | COHOMOLOGY | TRIPLES | ARTINIAN ALGEBRAS | COMMUTATOR | PAIRS | SCHEMES
Journal Article
Journal of Algebra, ISSN 0021-8693, 01/2015, Volume 422, pp. 611 - 632
...) by using the orbits of GL(n−1,C) on the flag variety B of gl(n,C). More precisely, let b... 
K-orbits on flag variety | Algebraic group actions | MATHEMATICS | GELFAND-ZETLIN MODULES | FLAG VARIETY | PERSPECTIVE | ZEITLIN THEORY | NILPOTENT MATRICES | CLASSICAL MECHANICS | HOMOGENEOUS SPACES | SUBGROUPS
Journal Article
Pure and Applied Mathematics Quarterly, ISSN 1558-8599, 2016, Volume 12, Issue 2, pp. 183 - 223
For a connected, simply-connected complex simple algebraic group G, we examine a class of Hessenberg varieties associated with the minimal nilpotent orbit... 
Minimal nilpotent orbit | Hessenberg variety | Equivariant cohomology | MATHEMATICS | MATHEMATICS, APPLIED | minimal nilpotent orbit | equivariant cohomology
Journal Article
2019, Progress in Mathematics, ISBN 3030235300, Volume 330, 563
This volume, a celebration of Anthony Joseph's fundamental influence on classical and quantized representation theory, explores a wide array of current topics... 
Nilpotent Lie groups | Topological Groups, Lie Groups | Mathematics | Representations of Lie algebras
eBook
Proceedings of the American Mathematical Society, ISSN 0002-9939, 03/2016, Volume 144, Issue 3, pp. 1343 - 1350
... approach to these representations, using the method of coadjoint orbits and thus relating them to the stratifications of duals of nilpotent Lie algebras Pd89... 
Square integrable representation | Nilpotent Lie group | Semidirect product | MATHEMATICS | MATHEMATICS, APPLIED | NILPOTENT LIE-GROUPS | nilpotent Lie group | semidirect product
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2018, Volume 146, Issue 1, pp. 195 - 208
.... We give a version of this result for nilpotent groups of diffeomorphisms. We prove that a nilpotent group of 2-torus diffeomorphims has finite orbits when the group... 
Diffeomorphism | Finite orbit | Derived group | Global fixed point | Rotation vector | Homeomorphism | Nilpotent group | Lefschetz number | DIFFEOMORPHISMS | MATHEMATICS, APPLIED | finite orbit | diffeomorphism | MATHEMATICS | ABELIAN ACTIONS | derived group | MAPS | homeomorphism | global fixed point | nilpotent group | S-2 | FIXED-POINTS | SURFACES | Mathematics - Dynamical Systems
Journal Article
Expositiones Mathematicae, ISSN 0723-0869, 06/2019, Volume 37, Issue 2, pp. 104 - 144
This expository article is an introduction to the adjoint orbits of complex semisimple groups, primarily in the algebro-geometric and Lie-theoretic contexts, and with a pronounced emphasis... 
Adjoint orbit | Semisimple algebraic group | Secondary | Primary | MATHEMATICS | EQUIVARIANT COHOMOLOGY | REPRESENTATIONS | NAHMS EQUATIONS | SINGULARITIES | NILPOTENT ORBITS | HYPERKAHLER METRICS | QUOTIENT
Journal Article
Representation Theory of the American Mathematical Society, ISSN 1088-4165, 10/2016, Volume 20, Issue 15, pp. 419 - 450
... and a character u of Nu (see Section for definitions). For example, if G is k-quasisplit and u belongs to a regular orbit, then Nu is a maximal unipotent subgroup and u... 
Nilpotent orbits | Automorphic forms | Representations | Wave-front sets | MATHEMATICS | wave-front sets | UNIPOTENT ORBITS | FOURIER COEFFICIENTS | automorphic forms | AUTOMORPHIC-FORMS | SYMPLECTIC GROUPS | representations
Journal Article
Journal of Lie Theory, ISSN 0949-5932, 2017, Volume 27, Issue 1, pp. 1 - 42
This paper is about nilpotent orbits of reductive groups over local non-Archimedean fields... 
Howe's conjecture | Nilpotent orbits | Reductive groups over local non-Archimedean fields | LIE-ALGEBRAS | MATHEMATICS | K-TYPES | FIELDS | reductive groups over local non-Archimedean fields | CHARACTERS
Journal Article
Journal of Algebra, ISSN 0021-8693, 12/2015, Volume 443, pp. 33 - 48
In this note we investigate the normality of closures of orthogonal and symplectic nilpotent orbits in positive characteristic... 
Nilpotent orbit closures | Normality | Orthogonal symplectic groups | MATHEMATICS | MATRICES | VARIETIES | CONJUGACY CLASSES
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 12/2013, Volume 365, Issue 12, pp. 6499 - 6515
Let G be the real symplectic group Sp(2n,ℝ). This paper determines the global sections of certain line bundles over the spherical nilpotent K ℂ -orbit 𝓞... 
Spherical nilpotent orbits | Vogan's conjecture | Admissible data | MATHEMATICS | REPRESENTATIONS | DEGENERATE PRINCIPAL SERIES | spherical nilpotent orbits
Journal Article
Representation Theory of the American Mathematical Society, ISSN 1088-4165, 10/2018, Volume 22, Issue 7, pp. 202 - 222
This paper provides a comparison between the K-structure of unipotent representations and regular sections of bundles on nilpotent orbits for complex groups of type D... 
Orthogonal groups | Nilpotent orbits | Infinte dimensional representations | MATHEMATICS | nilpotent orbits | DIRAC COHOMOLOGY | UNIPOTENT REPRESENTATIONS | orthogonal groups
Journal Article
Journal of Lie Theory, ISSN 0949-5932, 2018, Volume 28, Issue 2, pp. 323 - 341
The main purpose of this paper is to modify the orbit method for the Baum-Connes conjecture as developed by Chabert, Echterhoff and Nest in their proof... 
Orbit method | Baum-Connes conjecture | Local function fields | Linear algebraic groups | BIVARIANT K-THEORY | MATHEMATICS | EXACTNESS | COMPACT-GROUPS | NILPOTENT GROUPS | FOLIATIONS | NOVIKOV-CONJECTURE | linear algebraic groups | local function fields
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 2015, Volume 2015, Issue 3, pp. 787 - 816
... that are associated with flat coadjoint orbits. We use spaces of smooth symbols satisfying appropriate growth conditions expressed in terms of invariant differential operators on the coadjoint orbit under consideration... 
MATHEMATICS | NILPOTENT | PSEUDODIFFERENTIAL-OPERATORS
Journal Article
The Journal of Geometric Analysis, ISSN 1050-6926, 7/2019, Volume 29, Issue 3, pp. 2823 - 2861
... ∗ , taking the group structure into account and (c) Weyl-type quantizations of all the coadjoint orbits $$\big \{\Omega _\xi \mid \xi \in \widehat{{\textsf {G}}}\big \}$$ { Ω ξ ∣ ξ ∈ G... 
Pseudo-differential operator | Symbol | Mathematics | Weyl calculus | Abstract Harmonic Analysis | Secondary 22E30 | Fourier Analysis | Primary 22E25 | Convex and Discrete Geometry | Nilpotent group | 47G30 | Global Analysis and Analysis on Manifolds | Coadjoint orbit | Differential Geometry | Dynamical Systems and Ergodic Theory | Lie algebra | MATHEMATICS | INVARIANT PSEUDODIFFERENTIAL-OPERATORS | CALCULUS
Journal Article
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