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

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

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

... on the minimum numbers of generators, the numbers of orbits on k-partitions, and their normalizers in the symmetric group...

primitive groups | AUTOMORPHISM-GROUPS | GENERATORS | regular semigroups | PERMUTATION-GROUPS | ENDOMORPHISM SEMIGROUPS | CLASSIFICATION | NILPOTENT RANKS | MONOIDS | automorphisms of semigroups | CATEGORIES | Transformation semigroups | rank of semigroups | MATHEMATICS | homogeneous groups | permutation groups | TRANSITIVE COLLINEATION GROUPS | TRANSFORMATIONS

primitive groups | AUTOMORPHISM-GROUPS | GENERATORS | regular semigroups | PERMUTATION-GROUPS | ENDOMORPHISM SEMIGROUPS | CLASSIFICATION | NILPOTENT RANKS | MONOIDS | automorphisms of semigroups | CATEGORIES | Transformation semigroups | rank of semigroups | MATHEMATICS | homogeneous groups | permutation groups | TRANSITIVE COLLINEATION GROUPS | TRANSFORMATIONS

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

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

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

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

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

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

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

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

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

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

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

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

15.
Full Text
Normality of orthogonal and symplectic nilpotent orbit closures in positive characteristic

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

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

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

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

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

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

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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