arXiv research

Researchers describe local properties of Haantjes operators.

Random Forests adapted for dependent data using GLS.

Simplified computation of symmetric gl_1 homology for links.

Study flat GL(1|1) connections using fatgraphs and coordinates.

An almost Clifford and an almost Cliffordian manifold is a $G$--structure based on the definition of Clifford algebras. An almost Clifford manifold based on $\mathcal O:= \cc l (s,t)$ is given by a reduction of the structure group $GL(km, \mathbb R)$ to $GL(m, {\mathcal O})$, where $k=2^{s+t}$ and $m \in \mathbb N$. An…

We consider rank 3 distributions with growth vector (3,5,6). The class of such distributions splits into three subclasses: parabolic, hyperbolic and elliptic. In the present paper, we deal with the parabolic case. We provide a classification of such distributions and exhibit connections between them and Gl(2)-structure…

The paper constructs compatible Poisson brackets on gl(N).

We present state sums for quantum link invariants arising from the representation theory of $U_q(\mathfrak{gl}_{N|M})$. We investigate the case of the $N$-th exterior power of the standard representation of $U_q(\mathfrak{gl}_{N|1})$ and explicit the relation with Kashaev invariants.

New GLS estimator handles high-dimensional data with autocorrelated errors.

Study on $GL(1|1)$ Higgs bundles over Riemann surfaces.

Using quantum skew-Howe duality, we study the category $\operatorname{Rep}(\mathfrak{gl}(m|n))$ of tensor products of exterior powers of the standard representation of $U_q(\mathfrak{gl}(m|n))$, and prove that it is equivalent to a category of ladder diagrams modulo one extra family of relations. We then construct a ca…

The paper connects GL-racks to knot coloring invariants.

Researchers calculate dimensions of skein modules for 2-torus mapping tori.

Extends gl(m|k) construction using Hilbert scheme of points.

Study of generalized Legendrian racks and their GL-structures.

We consider various notions of strains; quantitative measures for the deviation of a linear transformation from an isometry. The main approach, which is motivated by physical applications and follows the work of Patrizio Neff and co-workers , is to select a Riemannian metric on $\text{GL}_n$, and use its induced geodes…

This paper is concerned about sparse, continuous frequency estimation in line spectral estimation, and focused on developing gridless sparse methods which overcome grid mismatches and correspond to limiting scenarios of existing grid-based approaches, e.g., $\ell_1$ optimization and SPICE, with an infinitely dense grid…

An differential field $(F;\partial_1,...,\partial_m)$ of characteristic zero, a subgroup $H$ of affine group $GL(n,C)\propto C^n$ with respect to its identical representation in $F^n$ and the following two fields of differential rational functions in $x=(x_1,x_2,...,x_n)$-column vector, $$C< x, \partial >^H=\{f^{\part…

We study five dimensional geometries associated with the 5-dimensional irreducible representation of GL(2,R). These are special Weyl geometries in signature (3,2) having the structure group reduced from CO(3,2) to GL(2,R). The reduction is obtained by means of a conformal class of totally symmetric 3-tensors. Among all…

Consider a finite dimensional (generally reducible) polynomial representation ρof GL_n. A projective compactification of GL_n is the closure of ρ(GL_n) in the space of all operators defined up to a factor (this class of spaces can be characterized as equivariant projective normal compactifications of GL_n). We give an …

We study $GL(2)$-structures on differential manifolds. The structures play a fundamental role in the geometric theory of ordinary differential equations. We prove that any $GL(2)$-structure on an even dimensional manifold give rise to a certain almost-complex structure on a bundle over the original manifold. Further, w…

Researchers compute $\mathfrak{gl}_2$-skein modules for lens spaces.

We provide an easy approach to the geodesic distance on the general linear group GL(n) for left-invariant Riemannian metrics which are also right-O(n)-invariant. The parametrization of geodesic curves and the global existence of length minimizing geodesics are deduced using simple methods based on the calculus of varia…

The study classifies and normalizes 3D gl-regular Nijenhuis operators.

We solve the regularized Knizhnik-Zamolodchikov equation and find an explicit expression for the Drinfeld associator. We restrict to the case of the fundamental representation of $gl(N)$. Several tests of the results are presented. It can be explicitly seen that components of this solution for the associator coincide w…

Study on GL(2) geometries on complex manifolds, focusing on Kähler-Einstein and Fano manifolds.

The object of this paper is to study GL(2,R) orbit closures in hyperelliptic components of strata of abelian differentials. The main result is that all higher rank affine invariant submanifolds in hyperelliptic components are branched covering constructions, i.e. every translation surface in the affine invariant subman…

We construct a canonical frame for an arbitrary Gl(2)-structure thus solving the equivalence problem for Gl(2)-structures. Our treatment includes also a problem of contact equivalence of ordinary differential equations and applies to certain classes of vector distributions. Additionally we characterise Gl(2)-structures…

Develops RF-GLS for binary geospatial data.

We construct a right-invariant differential calculus on the quantum supergroup GL$_h(1| 1)$ and obtain the $h$-deformed superalgebra of GL$_h(1| 1)$.

Class I CR manifolds have initial G-structure a certain 4-dimensional subgroup of GL_3(C). Class II CR manifolds have initial G-structure a certain 10-dimensional subgroup of GL_4(C). Class III-1 CR manifolds have initial G-structure a certain 10-dimensional subgroup of GL_5(C). Class III-2 CR manifolds have initial G-…

New basis for quantum gl_N invariants derived from Macdonald polynomials.

New homology for links in annulus discovered.

Study GLS estimator properties in multivariate regression with heteroskedastic and autocorrelated errors.

We study critical points of the Ginzburg-Landau (GL) functional and the abelian Yang-Mills-Higgs (YMH) functional on the sphere and the complex projective space, both equipped with the standard metrics. For the GL functional we prove that on $S^{n}$ with $n \geq 2$ and $\mathbb{CP}^{n}$ with $n \geq 1$, stable critical…

Extended quantum state result for gl_n weight systems.

In this paper we define an explicit basis for the $\mathfrak{gl}_n$-web algebra $H_n(\vec{k})$ (the $\mathfrak{gl}_n$ generalization of Khovanov's arc algebra) using categorified $q$-skew Howe duality. Our construction is a $\mathfrak{gl}_n$-web version of Hu--Mathas' graded cellular basis and has two major application…

The two-parametric quantum deformation of the algebra of coordinate functions on the supergroup GL$(1| 1)$ via a contraction of GL$_{p,q}(1| 1)$ is presented. Related differential calculus on the quantum superplane is introduced.

In previous work, we have constructed diagrammatic idempotents in an affine extension of the Temperley-Lieb category, which describe extremal weight projectors for sl(2), and which categorify Chebyshev polynomials of the first kind. In this paper, we generalize the construction of extremal weight projectors to the case…

A novel approach using graph learning and synthetic long positions for statistical arbitrage in options markets.

This article is a local analysis of integrable GL(2)-structures of degree 4. A GL(2)-structure of degree n corresponds to a distribution of rational normal cones over a manifold M of dimension (n+1). Integrability corresponds to the existence of many submanifolds that are spanned by lines in the cones. These GL(2)-stru…

In this paper, we consider the Graphical Lasso (GL), a popular optimization problem for learning the sparse representations of high-dimensional datasets, which is well-known to be computationally expensive for large-scale problems. Recently, we have shown that the sparsity pattern of the optimal solution of GL is equiv…

Paper defines and computes a new weight system for gl_N Lie algebra.

It is known that the level $2$ principal congruence subgroup of $GL(n;\mathbb{Z})$ has a finite generating set. In this paper, we give a finite presentation of the level $2$ principal congruence subgroup of $GL(n;\mathbb{Z})$.

Study of Hitchin map on specific Higgs bundles.

Study on holonomy of Obata connection on Joyce hypercomplex manifolds.

This paper studies gl-regular Nijenhuis operators and their properties.

The purpose of this paper is to study the Plancherel formula for the spaces of $L^2$-sections of the line bundles over the pseudo-Riemannian space $G/H$, where $G={\rm SL}(n+1, {\mathbb R})$ and $H={\rm S}({\rm GL}(1, {\mathbb R})\times {\rm GL}(n, {\mathbb R}))$. The formula is given in an explicit form by means of sp…