Related papers: Minimal semisimple Hessenberg schemes
In this paper, we find determinant formulas of several Hessenberg-Toeplitz matrices whose nonzero entries are derived from the small and large Schroder and Fine number sequences. Algebraic proofs of these results can be given which make use…
Based on recent advances on the relation between geometry and representation theory, we propose a new approach to elliptic Schubert calculus. We study the equivariant elliptic characteristic classes of Schubert varieties of the generalized…
Much of modern Schubert calculus is centered on Schubert varieties in the complete flag variety and on their classes in its integral cohomology ring. Under the Borel isomorphism, these classes are represented by distinguished polynomials…
We show that every non-compact simple real Lie algebra not isomorphic to so(n,1) has a unique conjugacy class of parabolic subalgebras whose nilradical is of Heisenberg type, or non-singular, and give some applications.
A minimal presentation of the cohomology ring of the flag manifold $GL_n/B$ was given in [A. Borel, 1953]. This presentation was extended by [E. Akyildiz-A. Lascoux-P. Pragacz, 1992] to a non-minimal one for all Schubert varieties. Work of…
For an endomorphism $s:V\rightarrow V$ of a finite dimensional complex vector space and an action of a torus $T$ on the full flag variety $\text{GL}_n({\mathbb C})/B$, we give a description of its fixed point set when $s$ is semisimple or…
In this paper, we introduce a reduction of a matrix to a condensed form, the upper $J$- Hessenberg form, via elementary symplectic Householder transformations, which are rank-one modification of the identity . Features of the reduction are…
The Deligne-Simpson problem (DSP) (resp. the weak DSP) is formulated like this: {\em give necessary and sufficient conditions for the choice of the conjugacy classes $C_j\subset GL(n,{\bf C})$ or $c_j\subset gl(n,{\bf C})$ so that there…
We reconsider a class of heterotic string theories studied in 1989, based on tensor products of N=2 minimal models with asymmetric simple current invariants. We extend this analysis from (2,2) and (1,2) spectra to (0,2) spectra with SO(10)…
In this paper we study some geometric properties of surfaces in the Heisenberg group, $\mathcal{H}_{3}.$ We obtain, using the Gauss map for Lie groups, a partial classification of minimal graphs in $\mathcal{H}_{3}.$ We also proof the non…
For a semisimple adjoint algebraic group $G$ and a Borel subgroup $B$, consider the double classes $BwB$ in $G$ and their closures in the canonical compactification of $G$: we call these closures large Schubert varieties. We show that these…
Peterson varieties are a special class of Hessenberg varieties that have been extensively studied e.g. by Peterson, Kostant, and Rietsch, in connection with the quantum cohomology of the flag variety. In this manuscript, we develop a…
We present a method for computing the Hilbert series of the algebra of invariants of the complex symplectic and orthogonal groups acting on graded noncommutative algebras with homogeneous components which are polynomial modules of the…
This article explores the relationship between Schubert varieties and equivariant embeddings, using the framework of homogeneous fiber bundles over flag varieties. We show that the homogenous fiber bundles obtained from…
We generalize the classical Henneberg minimal surface by giving an infinite family of complete, finitely branched, non-orientable, stable minimal surfaces in $\mathbb{R}^3$. These surfaces can be grouped into subfamilies depending on a…
We establish Bernstein Theorems for Lagrangian graphs which are Hamiltonian minimal or have conformal Maslov form. Some known results of minimal (Lagrangian) submanifolds are generalized.
Peterson varieties are subvarieties of flag varieties and their (equivariant) cohomology rings are given by Fukukawa-Harada-Masuda in type A and soon later the author with Harada and Masuda gives an explicit presentation of the…
We compare the following three families of geometric objects: Schubert varieties in flag manifolds, matrix Schubert varieties, and Borel orbits of 2-nilpotent matrices. The first family is governed by permutations, the second by partial…
We use the cylindrical homomorphism and a geometric construction introduced by J. Lewis to study the Lawson homology groups of certain hypersurfaces $X\subset \mathbb{P}^{n+1}$ of degree $d\leq n+1$. As an application, we compute the…
We show that in type A or C any degenerate flag variety is in fact isomorphic to a Schubert variety in an appropriate partial flag manifold.