Related papers: Notes on symmetrization by Bezoutiant

We consider H\"older continuous cocycles over an accessible partially hyperbolic system with values in the group of diffeomorphisms of a compact manifold $M$. We obtain several results for this setting. If a cocycle is bounded in…

We prove that the hyperbolicity cones of elementary symmetric polynomials are spectrahedral, i.e., they are slices of the cone of positive semidefinite matrices. The proof uses the matrix--tree theorem, an idea already present in Choe et…

We relate the combinatorics of Hall-Littlewood polynomials to that of abelian $p$-groups with alternating or Hermitian perfect pairings. Our main result is an analogue of the classical relationship between the Hall algebra of abelian…

Let $K$ be a field, $R=K[x, y]$ the polynomial ring and $\mathcal{M}(K)$ the set of all pairs of square matrices of the same size over $K.$ Pairs $P_1=(A_1,B_1)$ and $P_2=(A_2,B_2)$ from $\mathcal{M}(K)$ are called similar if…

This paper is partly a survey of known results on quadratic forms that are hard to find in the literature. Our main focus is a twisted form of a construction due to Bezout. This skew Bezoutian is a symplectic (resp. quadratic) space…

We give explicit polynomial-sized (in $n$ and $k$) semidefinite representations of the hyperbolicity cones associated with the elementary symmetric polynomials of degree $k$ in $n$ variables. These convex cones form a family of…

We show that for supersingular prime p the image of a unique meromorphic function G_p on X_0(p) (of degree two, with polar divisor {[0]_0,[\infty]_0}) under a certain Hecke operator is equal to j(\tau) (up to some additional constant). This…

Polynomials in a category have been studied as a generalization of the traditional notion in mathematics. Their construction has recently been extended to higher groupoids, as formalized in homotopy type theory, by Finster, Mimram, Lucas…

In this paper, we give some new identities of symmetry for q-Bernoulli polynomials under the symmetric group of degree n arising from p-adic q-integrals on Zp.

We describe three different approaches to the extended (N=2) supersymmetrization of the multicomponent KP hierarchy. In the first one we utilize only superfermions while in the second only superbosons and in the third superbosons as well as…

Given a symmetrizable Kac-Moody algebra $\mathfrack{g}$, we study its $\pi$-systems, which are subsets of real roots, the pairwise differences of whose elements are not roots. Such systems arise as simple systems of regular subalgebras of…

We study sets of univariate hyperbolic polynomials that share the same first few coefficients and show that they have a natural combinatorial description akin to that of polytopes. We define a stratification of such sets in terms of root…

A new two-parameter family of quasi-exactly solvable quartic polynomial potentials $V(x)=-x^4+2iax^3+(a^2-2b)x^2+2i(ab-J)x$ is introduced. Until now, it was believed that the lowest-degree one-dimensional quasi-exactly solvable polynomial…

We analyze the resolvent and define the scattering matrix for asymptotically hyperbolic manifolds with metrics which have a polyhomogeneous expansion near the boundary, and also prove that there is always an essential singularity of the…

Let g be a complex semisimple Lie algebra and let G' be the Langlands dual group. We give a description of the cohomology algebra of an arbitrary spherical Schubert variety in the loop Grassmannian for G' as a quotient of the form…

We calculate the homology of three families of 2-step nilpotent Lie (super)algebras associated with the symplectic, orthogonal, and general linear groups. The symplectic case was considered by Getzler and the main motivation for this work…

An element [\Phi] of the Grassmannian of n-dimensional subspaces of the Hardy space H^2, extended over the field C(x_1,..., x_n), may be associated to any polynomial basis {\phi} for C(x). The Pl\"ucker coordinates…

The $p$-norm of $r$-matrices generalizes the $2$-norm of $2$-matrices. It is shown that if a nonnegative $r$-matrix is symmetric with respect to two indices $j$ and $k$, then the $p$-norm is attained for some set of vectors such that the…

We resolve a problem of finding the Poincare symmetries from hamiltonian gauge symmetries constructed through a canonical procedure of handling constrained systems. Through the use of Noether identities corresponding to the symmetries, we…

The Poincar\'e polynomial of a Weyl group calculates the Betti numbers of the projective homogeneous space $G/B$, while the $h$-vector of a simple polytope calculates the Betti numbers of the corresponding rationally smooth toric variety.…