Related papers: A q-analogue of de Finetti's theorem

I present a $q$-analog of the discrete Painlev\'e I equation, and a special realization of it in terms of $q$-orthogonal polynomials.

Let F* be the field of q elements and let P(n,q) denote the projective space of dimension n-1 over F*. We construct a family H^{n}_{k,i} of combinatorial homology modules associated to P(n,q) for a coefficient field F of positive…

We consider in detail an approach (proposed by the author earlier) where quantum states are described by elements of a linear space over a Galois field, and operators of physical quantities - by linear operators in this space. The notion of…

We construct the q-analogue of Euler-Barnes' numbers and polynomials, and investigate their some properties.

We find two-sided inequalities for the generalized hypergeometric function of the form ${_{q+1}}F_{q}(-x)$ with positive parameters restricted by certain additional conditions. Both lower and upper bounds agree with the value of…

We introduce a probability distribution Q on the group of permutations of the set Z of integers. Distribution Q is a natural extension of the Mallows distribution on the finite symmetric group. A one-sided infinite counterpart of Q,…

We prove $q$-analogues of identities that are equivalent to the functional equation of the arithmetic-geometric mean. We also present $q$-analogues of $F(\sqrt{k},\frac{\pi}{2})$, the complete elliptical integral of the first kind, and its…

Associated with the fundamental representation of a quantum algebra such as $U_q(A_1)$ or $U_q(A_2)$, there exist infinitely many gauge-equivalent $R$-matrices with different spectral-parameter dependences. It is shown how these can be…

Let F be a finitely generated field of characteristic zero and \Gamma<GL_n(F) a finitely generated subgroup. For an element g in \Gamma, let Gal(F(g)/ F) be the Galois group of the splitting field of the characteristic polynomial of g over…

We prove some new results and unify the proofs of old ones involving complete monotonicity of expressions involving gamma and $q$-gamma functions, $0 < q < 1$. Each of these results implies the infinite divisibility of a related probability…

We discuss the structure of the endomorphism algebras of the jacobians of superelliptic curves y^q=f(x) where q is a prime power and f(x) is an irreducible cubic or quartic polynomial over the field of rational functions k(t) in…

Let $F$ be a field of prime characteristic $p$ containing $F_{p^n}$ as a subfield. We refer to $q(X)=X^{p^n}-X-a\in F[X]$ as a generalized Artin-Schreier polynomial. Suppose that $q(X)$ is irreducible and let $C_{q(X)}$ be the companion…

We study the restricted form of the qaunatized enveloping algebra of an untwisted affine Lie algebra and prove a triangular decomposition for it. In proving the decomposition we prove several new identities in the quantized algebra, one of…

Let $\ell$ be a prime number and let $F$ be a number field and $E/F$ a non-CM elliptic curve with a point $\alpha \in E(F)$ of infinite order. Attached to the pair $(E,\alpha)$ is the $\ell$-adic arboreal Galois representation…

If K/F is a finite abelian Galois extension of global fields whose Galois group has exponent t, we prove that there exists a short exact sequence that has as a consequence that if t is square free, then Dec(K/F)=Br_{t}(K/F) which we use to…

In this paper we present the following two results: we give an explicit description of the space of orderings of the field Q(x) as an inverse limit of finite spaces of orderings and we provide a new, simple proof of the fact that the class…

There studed correspondence between symplectic leaves, irreducible representations and prime ideals, which is invariant with respect to quantum adjoint action. The Conjecture of De Concini-Kac-Procesi on dimensions of irreducible…

We compute the $RO(G)$-graded equivariant algebraic $K$-groups of a finite field with an action by its Galois group $G$. Specifically, we show these $K$-groups split as the sum of an explicitly computable term and the well-studied…

This paper is on the inverse parameterized differential Galois problem. We show that surprisingly many groups do not occur as parameterized differential Galois groups over K(x) even when K is algebraically closed. We then combine the method…

We classify the coefficients $(a_1,...,a_n) \in \mathbb{F}_q[t]^n$ that can appear in a linear relation $\sum_{i=1}^n a_i \gamma_i =0$ among Galois conjugates $\gamma_i \in \overline{\mathbb{F}_q(t)}$. We call such an $n$-tuple a Smyth…