Related papers: Determinantal representations of semi-hyperbolic p…

We determine which quadratic polynomials in three variables are expanders over an arbitrary field $\mathbb{F}$. More precisely, we prove that for a quadratic polynomial $f\in \mathbb{F}[x,y,z]$, which is not of the form $g(h(x)+k(y)+l(z))$,…

We consider the algebra $R$ generated by three elements $A,B,H$ subject to three relations $[H,A]=A$, $[H,B]=-B$ and $\{A,B\}=f(H)$. When $f(H)=H$ this coincides with the Lie superalgebra $osp(1/2)$; when $f$ is a polynomial we speak of…

In this paper we extend the construction of special representations to Gromov hyperbolic groups which admits complementary series. We prove that these representations have a natural non-trivial reduced cohomology class $[c]$. An analogue of…

Define the $n$-th fibotomic polynomial to be the product of the monic irredicible factors of the $n$-th Fibonacci polynomial which are not factors of any Fibonacci polynomial of smaller degree. In this paper, we prove a number of properties…

We consider varieties of representations and characters of 2 and 3-dimensional orbifolds in semisimple Lie groups, and we focus on computing their dimension. For hyperbolic 3-orbifolds, we consider the component of the variety of characters…

With any integer convex polytope $P\subset\midR^n$ we associate a multivariate hypergeometric polynomial whose set of exponents is $\midZ^{n}\cap P.$ This polynomial is defined uniquely up to a constant multiple and satisfies a holonomic…

Label inventories for fine-grained entity typing have grown in size and complexity. Nonetheless, they exhibit a hierarchical structure. Hyperbolic spaces offer a mathematically appealing approach for learning hierarchical representations of…

In this paper, we use partial differential equations to find the decomposition of the polynomial algebra over the basic irreducible module of $E_7$ into a sum of irreducible submodules. Moreover, we obtain a combinatorial identity, saying…

We extend to several variables an earlier result of ours, according to which an entire function of one variable of sufficiently small exponential type, having all derivatives of even order taking integer values at two points, is a…

Poincare polinomials of hyperbolic Lie algebras, which are given by $HA_2$ and $HA_3$ in the Kac's notation, are calculated explicitly. The results show that there is a significant form for hyperbolic Poincare polinomials. Their explicit…

We consider the set of the power non-negative polynomials of several variables and its subset that consists of polynomials which can be represented as a sum of squares. It is shown in the classic work by D.Hilbert that it is a proper…

We develop a method to construct algebraic invariants for hypermatrices. We then construct hyperdeterminants and exhibit a generalization of the Cayley-Hamilton theorem for hypermatrices.

A pathway from one vertex of a quiver to another is a reduced path. We modify the classical definition of quiver representations and we prove that semi-invariant polynomials for filtered quiver representations come from diagonal entries if…

A classification of partially hyperbolic diffeomorphisms on 3-dimensional manifolds with (virtually) solvable fundamental group is obtained. If such a diffeomorphism does not admit a periodic attracting or repelling two-dimensional torus,…

We prove that every real nonnegative ternary quartic whose complex zero set is smooth can be represented as the determinant of a symmetric matrix with quadratic entries which is everywhere positive semidefinite. We show that the…

This work contains different expressions for the k'th derivative of the n'th power of the trigonometric and hyperbolic sine and cosine. The first set of expressions follow from the complex definitions of the trigonometric and hyperbolic…

A complete invariant and a binary combination for irreducible representations of SL2(R) are introduced. With this, a new two-parameter family of representations is defined.

We use the Whittaker vectors and the Drinfeld Casimir element to show that eigenfunctions of the difference Toda Hamiltonian can be expressed via fermionic formulas. Motivated by the combinatorics of the fermionic formulas we use the…

We introduce the general polynomial algebras characterizing a class of higher order superintegrable systems that separate in Cartesian coordinates. The construction relies on underlying polynomial Heisenberg algebras and their defining…

We prove an identity between three infinite families of polynomials which are defined in terms of `bosonic', `fermionic', and `one-dimensional configuration' sums. In the limit where the polynomials become infinite series, they give…