Related papers: Invariant multidimensional matrices

We consider the spin polynomial invariants for bundles with c_2=2 and c_1 = K_S + 2nk a rational mutiple of the canonical divisor on a Dolgacev surface. It is shown that the chamber structure can be controlled so that the polynomials give…

Let $E$ be an indecomposable rank two vector bundle on the projective space $\PP^n, n \ge 3$, over an algebraically closed field of characteristic zero. It is well known that $E$ is arithmetically Buchsbaum if and only if $n=3$ and $E$ is a…

Bound and scattering state Schr\"odinger functions of nonrelativistic quantum mechanics as representation matrix elements of space and time are embedded into residual representations of spacetime as generalizations of Feynman propagators.…

Let $n \in \mathbb{N}_{\geq 2}$. We prove that for every $k \geq 4$ there exist uniform but non-homogeneous Steiner bundles on $\mathbb{P}^n$ of $k$-type with disconnected splitting type, and we further investigate almost-uniform Steiner…

The paper presents the classification of matrix valued superpotentials corresponding to shape invariant systems of Schr\"odinger equations. All inequivalent irreducible matrix superpotentials realized by matrices of arbitrary dimension with…

A Steiner bundle over the projective 3-space is the kernel in a trivial bundle of a morphism defined by a matrix of linear forms. We produce various Steiner bundles E of rank n such that E(1) has n-1 sections, the dependency locus of which…

An orthogonal bundle over a curve has an isotropic Segre invariant determined by the maximal degree of a Lagrangian subbundle. This invariant, and the induced stratifications on moduli spaces of orthogonal bundles, were studied for bundles…

We introduce a multivariable Casson-Lin type invariant for links in $S^3$. This invariant is defined as a signed count of irreducible $\operatorname{SU}(2)$ representations of the link group with fixed meridional traces. For 2-component…

In this note we prove that the moduli space of rank $2n$ symplectic instanton bundles on ${\PP^{2n+1}}$, defined from the well known monad condition, is affine. This result was not known even in the case $n=1$, where the real instanton…

We define a Chern--Simons invariant of connections on stably trivial vector bundles over smooth manifolds, taking values in $3$-forms modulo closed forms with integral cohomology class. We show an additivity property of this invariant for…

We develop an invariant approach to $SU(2)$--structures on spin $5$--manifolds. We characterize (via spinor approach) the subspaces in the spinor bundle which induce the same group isomorphic to $SU(2)$. Moreover, we show how to induce…

The modular data of a modular category $\mathcal{C}$, consisting of the $S$-matrix and the $T$-matrix, is known to be an incomplete invariant of $\mathcal{C}$. More generally, the invariants of framed links and knots defined by a modular…

We construct a sequence of rank-$n$ indecomposable vector bundles on $\mathbb P^n\times\mathbb P^n$ for every $n\geq 2$ and in every positive characteristic that are not pullbacks via any map $\mathbb P^n\times\mathbb P^n\to \mathbb P^{m} $

Let $X$ be a differentiable manifold endowed with a transitive action $\alpha:A\times X\longrightarrow X$ of a Lie group $A$. Let $K$ be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms…

In this paper nondegenerate multidimensional matrices of boundary format in $V_0 \otimes ... \otimes V_p$ are investigated by their link with Steiner vector bundles on product of projective spaces. For any nondegenerate matrix $A$ the…

Over an algebraically closed base field $k$ of characteristic 2, the ring $R^G$ of invariants is studied, $G$ being the orthogonal group O(n) or the special orthogonal group SO(n) and acting naturally on the coordinate ring $R$ of the…

The set of unrestricted homotopy classes $[M,S^n]$ where $M$ is a closed and connected spin $(n+1)$-manifold is called the $n$-th cohomotopy group $\pi^n(M)$ of $M$. Moreover it is known that $\pi^n(M) = H^n(M;\mathbb Z) \oplus \mathbb Z_2$…

We define an $SL_2(\mathbb{R})$-Casson invariant of closed 3-manifolds. We also observe procedures of computing the invariants in terms of Reidemeister torsions. We discuss some approach of giving the Casson invariant some gradings.

In this work, we characterize matrices of linear forms and constant rank, demonstrating that, under some natural assumptions, they are always associated with a syzygy bundle that fits into a (partially linear) resolution. Furthermore, this…

The quantum concurrence of $SU(2) \otimes SU(2)$ spin-parity states is shown to be invariant under $SO(1,3)$ Lorentz boosts and $O(3)$ rotations when the density matrices are constructed in consonance with the covariant probabilistic…