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We consider geometric numerical integration algorithms for differential equations evolving on symmetric spaces. The integrators are constructed from canonical operations on the symmetric space, its Lie triple system (LTS), and the…
In this work, we study multiplicity-free induced representations of finite groups. We analyze in great detail the structure of the Hecke algebra corresponding to the commutant of an induced representation and then specialize to the…
Explicit expressions for multimatrix models with complex and unitary matrices allows to couple these models with well-known unitary, orthogonsl and sympletic ensembles. We consider examples of such mixed ensembles which are solvable in the…
It is known that optical activities can perform rotations. It is shown that the rotation, if modulated by attenuations, can perform symmetry operations of Wigner's little group which dictates the internal space-time symmetries of elementary…
We briefly describe the construction of a consistent $q$-deformation of the quantum mechanical isotropic harmonic oscillator on ordinary $\rn^N$ space.
The representation theory of the quantum group su$_q(2)$ is used to introduce $q$-analogues of the Wigner rotation matrices, spherical functions, and Legendre polynomials. The method amounts to an extension of variable separation from…
In the field of harmonic analysis, geometric considerations are frequently crucial. Specially, group actions such as translations, dilations and rotations on Euclidean space are instrumental. The objective of this paper is to extend the…
On the basis of the explicit formulae for the action of the unitary group of exponentials corresponding to almost solvable extensions of a given closed symmetric operator with equal deficiency indices, we derive a new representation for the…
We investigate orthogonal representations of compact Lie groups from the point of view of their quotient spaces, considered as metric spaces. We study metric spaces which are simultaneously quotients of different representations and…
This work is a contribution to the area of Strict Quantization (in the sense of Rieffel) in the presence of curvature and non-Abelian group actions. More precisely, we use geometry to obtain explicit oscillatory integral formulae for…
The elementary symmetric partition function is a map on the set of partitions. It sends a partition lambda to the partition whose parts are the summands in the evaluation of the elementary symmetric function on the parts of lambda. These…
Geometric symmetry induces symmetries of function spaces, and the latter yields a clue to global analysis via representation theory. In this note we summarize recent developments on the general theory about how geometric conditions affect…
Multiple-integral representations of the (skew-)Macdonald symmetric functions are obtained. Some bosonization schemes for the integral representations are also constructed.
We review and introduce several approaches to the study of centralizer algebras of the infinite symmetric group $S_\infty$. Our study is led by the double commutant relationships between finite symmetric groups and partition algebras; each…
We study symplectic groups and indefinite orthogonal groups over involutive, possibly noncommutative, algebras $(A, \sigma)$. In the case when the algebra $(A, \sigma)$ is Hermitian, or the complexification $(A_{\mathbb{C}},…
We construct a quadratic Morse-Bott function on the real Grassmannian of a symplectic vector space from a compatible linear complex structure. We show that its critical loci consist of linear subspaces that split into isotropic and complex…
We study noncommutative versions of holomorphic and harmonic functions on the unit disk.
After a brief survey of zeta function regularization issues and of the related multiplicative anomaly, illustrated with a couple of basic examples, namely the harmonic oscillator and quantum field theory at finite temperature, an…
We investigate H\"ormander spectral multiplier theorems as they hold on $X = L^p(\Omega),\: 1 < p < \infty,$ for many self-adjoint elliptic differential operators $A$ including the standard Laplacian on $\R^d.$ A strengthened matricial…
We develop an abstract framework for the investigation of quantization and dequantization procedures based on orthogonality relations that do not necessarily involve group representations. To illustrate the usefulness of our abstract method…