Horn recursion is a term used to describe when non-vanishing products of Schubert classes in the cohomology of complex flag varieties are characterized by inequalities parameterized by similar non-vanishing products in the cohomology of “smaller” flag varieties. We consider the type A partial flag variety and find that its cohomology exhibits a Horn recursion on a certain deformation of the cup...

It is proven that up to possible surface terms, the only non-vanishing momentum-dependent amplitudes for the self-dual N=2 string in R 2,2 are the tree-level two and three-point functions, and the only non-vanishing momentum-independent amplitudes are the one-loop partition function and the tree-level two and four-point functions. The calculations are performed using the topological prescriptio...

Horn recursion is a term used to describe when non-vanishing products of Schubert classes in the cohomology of flag varieties G/P are characterized by inequalities parameterized by similar non-vanishing products in the cohomology of ”smaller” flag varieties. We consider the partial flag variety SLn/P and find that H (SLn/P ) exhibits Horn recursion on a certain deformation of the cup product. W...

We give conceptual proofs of some well known results concerning compact non-positively curved locally symmetric spaces. We discuss vanishing and non-vanishing of Pontrjagin numbers and Euler characteristics for these locally symmetric spaces. We also establish vanishing results for StiefelWhitney numbers of (finite covers of) the Gromov-Thurston examples of negatively curved manifolds. We menti...

The efficient sensing of weak environmental perturbations via special degeneracies called exceptional points in non-Hermitian systems has attracted enormous attention the last few decades. However, contrast to extensive literature on parity-time (PT) symmetric systems, exotic hallmarks anti-PT are only beginning be realized now. Very recently, a characteristic resonance vanishing linewidth was ...

The purpose of the current paper is to introduce some new methods for studying the p-adic Banach spaces introduced by Emerton [9]. We first relate these spaces to more familiar sheaf cohomology groups. As an application, we obtain a more general version of Emerton’s spectral sequence. We also calculate the spaces in some easy cases. As a consequence, we obtain a number of vanishing theorems.

In this paper, we show that the class of R-quadratic Finsler spaces is a proper subset of the class of generalized Douglas-Weyl spaces. Then we prove that all generalized Douglas-Weyl spaces with vanishing Landsberg curvature have vanishing the non-Riemannian quantity H, generalizing result previously only known in the case of R-quadratic metric. Also, this yields an extension of well-known Num...

The total Hamiltonian in general relativity, which involves the first class and momentum constraints, weakly vanishes. However, when action is expanded around a classical solution as case of single scalar field inflationary model, there appears non-vanishing additional constraints; but this time theory becomes perturbative number fluctuation fields. We show that one can reorganize expansion sol...

In this paper we analyze the perturbations of the Kerr-Newman dilatonic black hole background. For this purpose we perfom a double expansion in both the background electric charge and the wave parameters of the relevant quantities in the Newman-Penrose formalism. We then display the gravita-tional, dilatonic and electromagnetic equations, which reproduce the static solution (at zero order in th...