arXiv research

The paper connects GL-racks to knot coloring invariants.

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

Study of generalized Legendrian racks and their GL-structures.

Study $GL(2)$-structures on manifolds leading to complex structures.

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 …

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

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

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

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…

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-…

Defines Khovanov homology with gl(1|1) action, preserving Reidemeister moves.

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

Proves metric equivalence for GL^+_n matrices.

New basis for quantum gl_N invariants derived from Macdonald polynomials.

Simplified computation of symmetric gl_1 homology for links.

Defines new $\mathfrak{gl}_2$-foams and their algebras, showing equivalence and applications.

New homology for links in annulus discovered.

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

The dualizing module of GL_n(O) varies, affecting cohomology vanishing and nonvanishing.

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.

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…

Random Forests adapted for dependent data using GLS.

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 cobrackets on flat GL(1, R)-bundles over surfaces, finding none for Turaev cobracket.

Classifies GL(2,R) invariant markings over Abelian differential components.

New method simplifies Graphical Lasso for chordal graphs.

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

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

In hyperelliptic components, GL(2,R) orbits are either closed, dense, or cover loci.

Paper proves Legendrian knots with same GL-rack have similar invariants.

Researchers describe local properties of Haantjes operators.

Four-dimensional GL(2) structures are flat with a specific subgroup transformation.

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

Classifies GL(2,R)-invariant subvarieties with zero Lyapunov exponents.

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…

We use the technique of quantum skew Howe duality to investigate the monoidal category of exterior powers of the standard representation of $U_q(\mathfrak{gl}(1|1))$. This produces a complete diagrammatic description of the category in terms of trivalent graphs, with the usual MOY relations plus one additional family o…

New structure for quantum algebra representations.

New invariant from Viro's gl(1|1) polynomial distinguishes lens spaces.

We introduce a construction of the differential calculus on the quantum supergroup GL$_{p,q}(1| 1)$. We obtain two differential calculi, respectively, associated with the left and right Cartan-Maurer one-forms. We also obtain the quantum superalgebra of GL$_{p,q}(1| 1)$. Although all of the structures we obtain are der…

Innovative rack theory applied to Legendrian links.

GL-LowPopArt improves minimax-optimal estimation for trace regression.

State sums for quantum link invariants from a specific representation.

We find generators for the full rational loop group of GL(n,C) as well as for the subgroup consisting of loops that satisfy the reality condition with respect to the noncompact real form GL(n,R). We calculate the dressing action of some of those generators on the positive loop group, and apply this to the ZS-AKNS flows…

Extremal weight projectors generalized for gl(N).