Related papers: Characters, Coadjoint Orbits and Duistermaat-Heckm…

We reconsider the problem of calculating a general spectral correlation function containing an arbitrary number of products and ratios of characteristic polynomials for a N x N random matrix taken from the Gaussian Unitary Ensemble (GUE).…

We present a conjecture (and a proof for G=SL(2)) generalizing a result of J. Arthur which expresses a character value of a cuspidal representation of a $p$-adic group as a weighted orbital integral of its matrix coefficient. It also…

To any finite group G of automorphisms of a symplectic vector space V we associate a new multi-parameter deformation, H_k, of the smash product of G with the polynomial algebra on V. The algebra H_k, called a symplectic reflection algebra,…

Following Boalch-Yamakawa and Meinrenken, we consider a certain class of moduli spaces on bordered surfaces from a quasi-Hamiltonian perspective. For a given Lie group $G$, these character varieties parametrize flat $G$-connections on…

When $G_{\mathbb{R}}$ is a real, linear algebraic group, the orbit method predicts that nearly all of the unitary dual of $G_{\mathbb{R}}$ consists of representations naturally associated to orbital parameters $(\mathcal{O},\Gamma)$. If…

Following the ideas of Ginzburg, for a subgroup $K$ of a connected reductive $\mathbb{R}$-group $G$ we introduce the notion of $K$-admissible $D$-modules on a homogeneous $G$-variety $Z$. We show that $K$-admissible $D$-modules are regular…

The character ring \CGL of covariant irreducible tensor representations of the general linear group admits a Hopf algebra structure isomorphic to the Hopf algebra \Sym$ of symmetric functions. Here we study the character rings \CO and \CSp…

We systematically study inhomogeneous Hamiltonians in two-dimensional conformal field theories within the framework of the AdS/CFT correspondence by relating them to two-dimensional curved backgrounds. We propose a classification of…

In the paper there are investigated various approximate representations of the infinite dimensional $\Bbb Z$--graded Lie algebras: the Witt algebra of all Laurent polynomial vector fields on a circle and its one-dimensional nontrivial…

In the finite-dimensional setting, every Hermitian-symmetric space of compact type is a coadjoint orbit of a finite-dimensional Lie group. It is natural to ask whether every infinite-dimensional Hermitian-symmetric space of compact type,…

In this paper we generalize some of these results for loop algebras and groups as well as for the Virasoro algebra to the two-dimensional case. We define and study a class of infinite dimensional complex Lie groups which are central…

We derive manifestly covariant actions of spinning particles starting from coadjoint orbits of isometry groups, by using Hamiltonian reductions. We show that the defining conditions of a classical Lie group can be treated as Hamiltonian…

Let K $\subset$ G be compact connected Lie groups with common maximal torus T. Let (M, $\omega$) be a prequantisable compact connected symplectic manifold with a Hamiltonian G-action. Geometric quantisation gives a virtual representation of…

Let $G$ be a semisimple Lie group with discrete series. We use maps $K_0(C^*_rG)\to \mathbb{C}$ defined by orbital integrals to recover group theoretic information about $G$, including information contained in $K$-theory classes not…

In this article we study asymptotic properties of certain discrete groups $\Gamma$ acting by isometries on a product $\XX=\XX_1\times \XX_2$ of locally compact Hadamard spaces. The motivation comes from the fact that Kac-Moody groups over…

Let $\mathfrak{g}$ be a simple finite dimensional complex Lie algebra and let $\widehat{\mathfrak{g}}$ be the corresponding affine Lie algebra. Kac and Wakimoto observed that in some cases the coefficients in the character formula for a…

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…

Let $G$ be a connected reductive $p$-adic group. As verified for unipotent representations, it is expected that there is a close relation between the (Harish-Chandra-Howe) wavefronts sets of irreducible smooth representations and their…

Consider a standard representation $\pi_{st}$ of a quasi-split reductive p-adic group G. The generalized injectivity conjecture, posed by Casselman and Shahidi, asserts that any generic irreducible subquotient $\pi$ of $\pi_{st}$ is…

The Adler Kostant Symes [A-K-S] scheme is used to describe mechanical systems for quadratic Hamiltonians of $\mathbb R^{2n}$ on coadjoint orbits of the Heisenberg Lie group. The coadjoint orbits are realized in a solvable Lie algebra…