Related papers: Involutions in $S_n$ and associated coadjoint orbi…

This thesis studies the symplectic structure of holomorphic coadjoint orbits, and their projections. A holomorphic coadjoint orbit O is an elliptic coadjoint orbit which is endowed with a natural invariant K\"ahlerian structure. These…

The symmetric group $\mathfrak{S}_n$ acts on the polynomial ring $\mathbb{Q}[\mathbf{x}_n] = \mathbb{Q}[x_1, \dots, x_n]$ by variable permutation. The invariant ideal $I_n$ is the ideal generated by all $\mathfrak{S}_n$-invariant…

In this paper we construct a deformation quantization of the algebra of polynomials of an arbitrary (regular and non regular) coadjoint orbit of a compact semisimple Lie group. The deformed algebra is given as a quotient of the enveloping…

In this paper we give an effective method for finding a unique representative of each orbit of the adjoint and coadjoint action of the real affine orthogonal group on its Lie algebra. In both cases there are orbits which have a modulus that…

Let $\mathfrak g$ be a classical simple Lie algebra over an algebraically closed field $\mathbb F$ of characteristic zero or large enough, and let $\mathfrak n$ be a maximal nilpotent subalgebra of $\mathfrak g$. The main tool in…

Let G be a simple algebraic group defined over an algebraically closed field of characteristic 0 or a good prime for G. Let U be a maximal unipotent subgroup of G and \u its Lie algebra. We prove the separability of orbit maps and the…

In this paper we construct quantum analogs of strata of coadjoint orbits and describe their representations. This kind objects play an important role in describing quantum groups as repeated extensions of quantum strata.

The purpose of this paper is to apply deformation quantization to the study of the coadjoint orbit method in the case of real reductive groups. We first prove some general results on the existence of equivariant deformation quantization of…

Kirillov's orbit theory provides a powerful tool for the investigation of irreducible unitary representations of many classes of Lie groups. In a previous paper we used a modification hereof, called monomial linearisation, to construct a…

The natural partial ordering of the orbit types of the action of the group of local gauge transformations on the space of connections in space-time dimension d<=4 is investigated. For that purpose, a description of orbit types in terms of…

The variety of complete quadrics is the wonderful compactification of $GL_n/O_n$ and admits a cell decomposition into Borel orbits indexed by combinatorial objects called $\mu$-involutions. We study Coxeter-theoretic properties of…

This is a thorough investigation on the real $K$-theory of the sphere $S^d$ associated with the antipodal involution. We calculate the algebraic structure of real $K$-theory and united $K$-theory for all $d$, we write down explicit…

Let G be a Lie group, $g = Lie(G)$ - its Lie algebra, $g*$ - the dual vector space and $\widehat G$ - the set of equivalence classes of unitary irreducible representations of $G$. The orbit method [1] establishes a correspondence between…

We provide an explicit construction of quasi-invariant measures on polarized coadjoint orbits of a Lie group G. The use of specific (trivial) central extensions of G by the multiplicative group ${R}^+$ allows us to restore the strict…

We present an explicit $\U_h\bigl(gl(n,\C)\bigr)$-equivariant quantization on coadjoint orbits of $GL(n,\C)$. It forms a two-parameter family quantizing the Poisson pair of the reflection equation and Kirillov-Kostant-Souriau brackets.

We study properties of convex hulls of (co)adjoint orbits of compact groups, with applications to invariant theory and tensor product decompositions. The notion of partial convex hulls is introduced and applied to define two numerical…

Our goal is to find a representative of each orbit of the coadjoint action of the generalized Galile group on the dual of its Lie algebra. Our line of argument follows that of Cushman and van der Kallen, but differs in the details.

In our previous paper, we constructed an explicit GL(n)-equivariant quantization of the Kirillov--Kostant-Souriau bracket on a semisimple coadjoint orbit. In the present paper, we realize that quantization as a subalgebra of endomorphisms…

These notes treat a momentum map associated to the Heisenberg group. We classify the coadjoint orbits of the Heisenberg group and show that the cocycle associated to the momentum map becomes a value of the modulus of a coadjoint orbit. We…

Let $V$ be a projective variety defined over a number field $K$, let $S$ be a polarized set of endomorphisms of $V$ all defined over $K$, and let $P\in V(K)$. For each prime $\mathfrak{p}$ of $K$, let $m_{\mathfrak{p}}(S,P)$ denote the…