Related papers: Hook fusion procedure for hyper-octahedral groups
We prove Horrocks' theorem for the odd elementary orthogonal group, which gives a decomposition of an orthogonal matrix with entries from a polynomial ring $R[X]$, over a commutative ring $R$ in which 2 is invertible, as a product of an…
We compute the cylindrical contact homology of the links of the simple singularities. These manifolds are contactomorphic to $S^3/G$ for finite subgroups $G\subset\text{SU}(2)$. We perturb the degenerate contact form on $S^3/G$ with a Morse…
The main purpose of this paper is to compute all irreducible spherical functions on $G={SL}(2,{\mathbb C})$ of arbitrary type $\delta\in \hat K$, where $K={SU}(2)$. This is accomplished by associating to a spherical function $\Phi$ on $G$ a…
In this paper, we give several matrix representations for the Horadam quaternions. We derive several identities related to these quaternions by using the matrix method. Since quaternion multiplication is not commutative, some of our results…
In this paper, an analytic approximation method for highly nonlinear equations, namely the homotopy analysis method (HAM), is employed to solve some backward stochastic differential equations (BSDEs) and forward-backward stochastic…
We classify all irreducible admissible representations of three Olshanski pairs connected to the infinite symmetric group. In particular, our methods yield two simple proofs of the classical Thoma's description of the characters of the…
We study a class of graph Hamiltonians given by a type of quiver representation to which we can associate (non)--commutative geometries. By selecting gauging data these geometries are realized by matrices through an explicit construction or…
We develop a new, group-theoretic approach to bounding the exponent of matrix multiplication. There are two components to this approach: (1) identifying groups G that admit a certain type of embedding of matrix multiplication into the group…
In this paper, we propose a hierarchical random compression method (HRCM) for kernel matrices in fast kernel summations. The HRCM combines the hierarchical framework of the H-matrix and a randomized sampling technique of the column and row…
This expository article presents a self-contained introduction to simplicial homology for finite simplicial complexes, emphasizing concrete computation and geometric intuition. Beginning with orientations of simplices and the construction…
Let H be a split reductive group over a local non-archimedean field, and let H^ denote its Langlands dual group. We present an explicit formula for the generating function of an unramified L-function associated to a highest weight…
An axiomatic approach to the representation theory of Coxeter groups and their Hecke algebras was presented in [1]. Combinatorial aspects of this construction are studied in this paper. In particular, the symmetric group case is…
In this paper we have considered a finite unitary matrix group with exact elements being unknown and only approximate elements available. Such a group becomes inconsistent with its own multiplication table. We found simple correction…
Connecting orbits are important invariant structures in the state space of nonlinear systems and various techniques are designed for their computation. However, a uniform analytic approximation of the whole orbit seems rare. Here, based on…
We compute invariants of quadratic forms associated to orthogonal hypergeometric groups of degree five. This allows us to determine some commensurabilities between these groups, as well as to say when some thin groups cannot be conjugate to…
This paper proposes a new approach to deriving a finite particle content, suitable for the construction of a gauge theory. Specifically, the outlined construction generates a finite set of irreducible gauge representations, which are…
A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to…
We show that Hopf invariants, defined by evaluation in Harrison cohomology of the commutative cochains of a space, calculate the logarithm map from a fundamental group to its Malcev Lie algebra. They thus present the zeroth Harrison…
The Hierarchical Dirichlet Process (HDP) provides a flexible Bayesian nonparametric framework for modeling grouped data with a shared yet unbounded collection of mixture components. While existing applications of the HDP predominantly focus…
We define basic notions in the category of conic representations of a topological group and prove elementary facts about them. We show that a conic representation determines an ordinary dynamical system of the group together with a…