arXiv research

SL(n) covariant valuations on Orlicz spaces are represented and characterized.

Classification of SL(n) covariant valuations on Orlicz spaces.

Classifies SL(n) covariant matrix-valued valuations on Lp-spaces.

Recently Berman and Perry constructed a four-dimensional M-theory effective action which manifests SL(5) U-duality. Here we propose an underlying differential geometry of it, under the name `SL(5) U-geometry' which generalizes the ordinary Riemannian geometry in an SL(5) compatible manner. We introduce a `semi-covarian…

We construct a duality manifest gravitational theory for the special linear group, ${\mathbf{SL}(N)}$ with $N{\neq 4}$. The spacetime is formally extended, to have the dimension $\textstyle{\frac{1}{2}} N(N-1)$, yet is `gauged'. Consequently the theory is subject to a section condition. We introduce a semi-covariant de…

The classical Rankin-Cohen brackets are bi-differential operators from $C^\infty(\mathbb R)\times C^\infty(\mathbb R)$ into $C^\infty(\mathbb R)$. They are covariant for the (diagonal) action of ${\rm SL}(2,\mathbb R)$ through principal series representations. We construct generalizations of these operators, replacing…

Following the point of view of Gray and Hervella, we derive detailed conditions which characterize each one of the classes of almost quaternion-Hermitian $4n$-manifolds, $n>1$. Previously, by completing a basic result of A. Swann, we give explicit descriptions of the tensors contained in the space of covariant derivati…

We find a unique torsion free Riemannian spin connection for the natural Killing metric on the quantum group $C_q[SL_2]$, using a recent frame bundle formulation. We find that its covariant Ricci curvature is essentially proportional to the metric (i.e. an Einstein space). We compute the Dirac operator and find for $q$…

In the present article, we combine some techniques in the harmonic analysis together with the geometric approach given by modules over sheaves of rings of twisted differential operators ($\mathcal{D}$-modules), and reformulate the composition series and branching problems for objects in the Bernstein-Gelfand-Gelfand pa…

This paper extends SLS controllers to two stocks, proving the RPE property with cross-coupling.

The group lasso is a penalized regression method, used in regression problems where the covariates are partitioned into groups to promote sparsity at the group level. Existing methods for finding the group lasso estimator either use gradient projection methods to update the entire coefficient vector simultaneously at e…

In this paper we show how to describe the general theory of a linear metric compatible connection with the theory of Clifford valued differential forms. This is done by realizing that for each spacetime point the algebra of Clifford bivectors is isomorphic to the Lie algebra of Sl(2,C). In that way the pullback of the …

Unified description of p-brane QP-manifolds connects two recent tensor hierarchy descriptions.

A correspondence between three-dimensional flat connections and constant curvature four-dimensional simplices is used to give a novel quantization of geometry via complex SL(2,C) Chern-Simons theory. The resulting quantum geometrical states are hence represented by the 3d blocks of analytically continued Chern-Simons t…

We study the classification of special almost hermitian manifolds in Gray and Hervella's type classes. We prove that the exterior derivatives of the symplectic form and the complex volume form contain all the information about the intrinsic torsion of the $\SUn(n)$-structure. Furthermore, we apply the obtained results …

Classifies limits of groups of involutions in SL(2,F) over local fields.

Define web algebras for annular SL(2) and SL(3) using foam TQFTs.

Classifies actions of SL(n,R) and SL(n,Z) on closed n-manifolds.

Study of Lagrangian submanifolds in pseudo-nearly Kähler SL(2,R)×SL(2,R).

We show the correspondence between left invariant flat projective structures on Lie groups and certain prehomogeneous vector spaces. Moreover by using the classification theory of prehomogeneous vector spaces, we classify complex Lie groups admitting irreducible left invariant flat complex projective structures. As a r…

Explicitly found generators of cohomology for SL_n(Z) using sharbly cycles and cosharbly cocycles.

Extends $sl(3)$ invariant to tangles via webs and functors.

We construct an equivariant colored sl(N)-homology for links, which generalizes both the colored sl(N)-homology defined by the author and the equivariant sl(N)-homology defined by Krasner. The construction is a straightforward generalization of that of the colored sl(N)-homology. The proof of invariance is based on a s…

The paper classifies topological properties of specific geometric forms on manifolds.

New sl(2) action defined on a mathematical module.

It is showed that many examples of AMD submanifolds of higher dimensions come from SL normal bundles. A symmetry property of SL submanifolds and Björling type problem for SL normal bundles are also mentioned.

Classifies real-analytic SL(n,R) actions on closed manifolds.

We construct a categorification of the quantum sl_3 projectors, the sl_3 analog of the Jones-Wenzl projectors, as the stable limit of the complexes assigned to k-twist torus braids (as k goes to infinity) in a suitably shifted version of Morrison and Nieh's geometric formulation of sl_3 link homology (math.GT/0612754).…

We study the Chabauty compactification of two families of closed subgroups of $SL(n,\mathbb{Q}_p)$. The first family is the set of all parahoric subgroups of $SL(n,\mathbb{Q}_p)$. Although the Chabauty compactification of parahoric subgroups is well studied, we give a different and more geometric proof using various Le…

Decomposes $SL_3$ skein algebras for surfaces.

The study proves non-existence of hypercomplex structures on SL(3,R) and finds one on SL(2n+1,C).

We define two functors from Elias and Khovanov's diagrammatic Soergel category, one targeting Clark-Morrison-Walker's category of disoriented sl(2) cobordisms and the other the category of (universal) sl(3) foams.

We classify SL(2;C)-representations of a Brieskorn homology 3-sphere. We show any irreducible representation into SL(2;C) is conjugate to that into either SU(2) or SL(2;R). We also give a construction of SL(2;R)-representations for a Brieskorn homology 3-sphere from PSL(2;R)-representations of the base orbifold fundame…

A first-order formulation of gravity is developed in which the fundamental fields consist of an SL(2,C) connection and two spinor-valued 1-forms. It is shown that the first term of an expansion of the Einstein-Hilbert action leads to an action for these fields which consists of dynamic L2 inner products of their covari…

Two specific Einstein metrics found on a product of SL(2,R) groups.

Odd-dimensional SL(n,Q) contains dense surface subgroups.

The paper calculates colored Jones polynomials for specific link configurations.

Given a finite volume hyperbolic 3-manifold, we compose a lift of the holonomy in SL(2,C) with the n-dimensional irreducible representation of SL(2,C) in SL(n,C). In this paper we give local coordinates of the SL(n,C)-character variety around this representation. As a corollary, this representation is isolated among al…

Study local limits of subgroups in $SL_3(\mathbb{R})$.

LLmFPCA-detect detects anomalies in sparse longitudinal text data using LLMs and mFPCA.

We introduce two invariants called sl(3) Khovanov module and pointed sl(3) Khovanov homology for spatial webs (bipartite trivalent graphs). Those invariants are related to Kronheimer-Mrowka's instanton invariants $J^\sharp$ and $I^\sharp$ for spatial webs by two spectral sequences. As an application of the spectral seq…

The paper constructs bases for cluster varieties using ${ m SL}_3$-webs and laminations.

Study on cohomology of SL_n(Z) for n>=3, proving vanishing of certain cohomology groups.

Lectures introduce evaluation of SL(3) foams and link homology.

The paper classifies totally geodesic Lagrangian submanifolds in a specific pseudo-nearly Kähler space.

Study SL(2,C) character schemes for finitely generated groups.

Extends knot invariant computation to symmetrically colored sl_N.

Paper proves zero stability for one-row colored sl₃-Jones polynomials.