Related papers: Normal and seminormal forms of sl(3)-valued zero c…

In this paper we give the classification of standard compact Clifford-Klein forms corresponding to triples (g,h,l) such that g = h+l and g is a sum of two absolutely simple ideals. The classification is done using Onishchik's results…

Recently we showed that Hessenberg matrices are proper to represent conjugacy classes in SL(n,Z). In this paper we focus on the reducibility properties in the set of Hessenberg matrices of SL(3,Z). We investigate the first interesting open…

This paper mainly focuses on the CR analogue of the three-circle theorem in a complete noncompact pseudohermitian manifold of vanishing torsion being odd dimensional counterpart of K\"ahler geometry. In this paper, we show that the CR…

Given a minuscule representation of a simple Lie algebra, we find an algebraic model for the action of a regular element and show that these models can be glued together over the adjoint quotient, viewed as the set of all regular conjugacy…

A manifold with an irreducible $SO(3)$-structure is a $5$-manifold $M$ whose structure group can be reduced to the group $SO(3)$, non-standardly imbedded in $SO(5)$. The study of such manifolds has been initiated by M. Bobie\'nski and P.…

This chapter is based on a series of lectures that I gave at the National University of Singapore in April 2013. The notes survey the representation theory of the cyclotomic Hecke algebras of type A with an emphasis on understanding the KLR…

In this paper we will be classifying some regular upper-triangular subalgebras of $\mathfrak{sl}(n, \mathbb C)$ up to conjugacy by matrices in $SL(n, \mathbb C)$. We do so for dimension 2, codimension 1, and codimension 2 subalgebras. We…

We investigate certain $Z_3$-graded associative algebras with cubic $Z_3$-invariant constitutive relations. The invariant forms on finite algebras of this type are given in the low dimensional cases with two or three generators. We show how…

For each finite subgroup G of SL(n, C), we introduce the generalized Cartan matrix C_{G} in view of McKay correspondence from the fusion rule of its natural representation. Using group theory, we show that the generalized Cartan matrices…

We shall discuss the class of surfaces with holomorphic right Gauss maps in non-compact duals of compact semisimple Lie groups (e.g. SL(n,C)/SU(n)), which contains minimal surfaces in R^n and constant mean curvature 1 surfaces in H^3. A…

We propose two constructions extending the Chern-Moser normal form to non-integrable Levi-nondegenerate (hypersurface type) almost CR structures. One of them translates the Chern-Moser normalization into pure intrinsic setting, whereas the…

Let S be the spectrum of a discrete valuation ring with function field K. Let X be a scheme over S. We will say that X is semi-factorial over S if each invertible sheaf on the generic fiber X_K can be extended to an invertible sheaf on X.…

Motivated by recent works in Levi degenerate CR geometry, this article endeavours to study the wider and more flexible para-CR structures for which the constraint of invariancy under complex conjugation is relaxed. We consider…

We know that semi-regular sub-varieties satisfy the variational Hodge conjecture i.e., given a family of smooth projective varieties $\pi:\mathcal{X} \to B$, a special fiber $\mathcal{X}_o$ and a semi-regular subvariety $Z \subset…

V.I. Arnold [Russian Math. Surveys 26(2) (1971) 29-43] constructed a miniversal deformation of a square complex matrix under similarity; that is, a simple normal form to which not only a given square matrix A but all matrices B close to it…

It is well known that the full matrix ring over a skew-field is a simple ring. We generalize this theorem to the case of semirings. We characterize the case when the matrix semiring $\mathbf{M}_n(S)$, of all $n\times n$ matrices over a…

Generalizing the concept of primary fields, we find a new representation of the Virasoro algebra, which we call it a pseudo-conformal representation. In special cases, this representation reduces to ordinary- or logarithmic-conformal field…

We study the behavior of representation varieties of quivers with relations under the operation of node splitting. We show how splitting a node gives a correspondence between certain closed subvarieties of representation varieties for…

In this paper we give a detailed classification scheme for three-dimensional quantum zero curvature representation and tetrahedron equations. This scheme includes both even and odd parity components, the resulting algebras of observables…

To demonstrate the discrepancy between second-order cone and semidefinite programming, Hamza Fawzi showed that the cone S_+^3 of symmetric positive semidefinite matrices of size 3 is not second-order cone representable (socr). A slice of…