Related papers: Representations of the infinite unitary group from…

In this paper, we begin a quantization program for nilpotent orbits of a real semisimple Lie group. These orbits and their covers generalize the symplectic vector space. A complex structure polarizing the orbit and invariant under a maximal…

Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general…

In this paper we explore the method of holomorphic induction for unitary representations of Banach--Lie groups. First we show that the classification of complex bundle structures on homogeneous Banach bundles over complex homogeneous spaces…

The standard (Berezin-Toeplitz) geometric quantization of a compact Kaehler manifold is restricted by integrality conditions. These restrictions can be circumvented by passing to the universal covering space, provided that the lift of the…

We study representations of the Cuntz algebras O_d and their associated decompositions. In the case that these representations are irreducible, their restrictions to the gauge-invariant subalgebra UHF_d have an interesting cyclic structure.…

We prove that the canonical dimension of a coadmissible representation of a semisimple $p$-adic Lie group in a $p$-adic Banach space is either zero or at least half the dimension of a non-zero coadjoint orbit. To do this we establish…

In this paper we are mainly concerned with the study of polarizations (in general of higher-order type) on a connected Lie group with a U(1)-principal bundle structure. The representation technique used here is formulated on the basis of a…

We propose a general framework to contract unitary dual of Lie groups via holomorphic quantization of their co-adjoint orbits. The sufficient condition for the contractability of a representation is expressed via cocycles on coadjoint…

Let M be a manifold with an action of a Lie group G, $\A$ the function algebra on M. The first problem we consider is to construct a $U_h(\g)$ invariant quantization, $\A_h$, of $\A$, where $U_h(\g)$ is a quantum group corresponding to G.…

This is the first in a series of papers devoted to an analogue of the metaplectic representation, namely, the minimal unitary representation of an indefinite orthogonal group; this representation corresponds to the minimal nilpotent…

We develop a relativistic framework of integral quantization applied to the motion of spinless particles in the four-dimensional Minkowski spacetime. The proposed scheme is based on coherent states generated by the action of the…

Let $G$ be a complex reductive algebraic group. In arXiv:2108.03453, we have defined a finite set of irreducible admissible representations of $G$ called `unipotent representations', generalizing the special unipotent representations of…

In this paper we study the variety of one dimensional representations of a finite $W$-algebra attached to a classical Lie algebra, giving a precise description of the dimensions of the irreducible components. We apply this to prove a…

Recently, it has been observed that a certain class of classical theories with constraints can be quantized by a mathematical procedure known as Rieffel induction. After a short exposition of this idea, we apply the new quantization theory…

We show that $\frak{su}(2)$ Lie algebras of coordinate operators related to quantum spaces with $\frak{su}(2)$ noncommutativity can be conveniently represented by $SO(3)$-covariant poly-differential involutive representations. We show that…

The main result of this article is an application of the theory of invariant convex cones of Lie algebras to the study of unitary representations of Lie supergroups. It also includes an exposition of recent results of the second author on…

We reconsider the quantization of symbols defined on the product between a nilpotent Lie algebra and its dual. To keep track of the non-commutative group background, the Lie algebra is endowed with the Baker-Campbell-Hausdorff product,…

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…

Let $X$ be a separable Banach space and let $Q:X^*\rightarrow X$ be a linear, bounded, non-negative and symmetric operator and let $A:D(A)\subseteq X\rightarrow X$ be the infinitesimal generator of a strongly continuous semigroup of…

We discuss the Kirillov method for massless Wigner particles, usually (mis)named "continuous spin" or "infinite spin" particles. These appear in Wigner's classification of the unitary representations of the Poincar\'e group, labelled by…