Related papers: Multitransgression and regulators

We introduce and study a category of algebras strongly connected with the structure of the Gelfand-Tsetlin subalgebras of the endomorphism algebras of Bott-Samelson bimodules. We develop a series of techniques that allow us to obtain…

In this note, we formulate and prove branching rules of simple polynomial modules for the Lie superalgebra $\mathfrak{gl}(m|n)$. Our branching rules depend on the conjugacy class of the Borel subalgebra. A Gelfand-Tsetlin basis of a…

We establish sharp inequalities involving the incomplete Beta and Gamma functions. These inequalities arise in the approximation of generalized Bernstein functions by higher order Thorin-Bernstein functions. Furthermore, new properties of a…

In this paper we propose a conseptual framework for the observed properties of discriminants of polylinear forms. The connection with classical problems of linear algebra is shown. A new class of algebraic varieties (hypergrassmanians) is…

A multifractal-like representation for multi-time multi-scale velocity correlation in turbulence and dynamical turbulent models is proposed. The importance of subleading contributions to time correlations is highlighted. The fulfillment of…

We carry out some algebraic and analytic properties of a new class of orthogonal polyanalytic polynomials, including their operational formulas, recurrence relations, generating functions, integral representations and different…

We describe a generalization of the notion of a Hilbert space model of a function in the Schur class of the bidisc. This generalization is well adapted to the investigation of boundary behavior at a mild singularity of the function on the…

Character polynomials are used to study the restriction of a polynomial representation of a general linear group to its subgroup of permutation matrices. A simple formula is obtained for computing inner products of class functions given by…

The paper deals with the problem of approximating the functions of several variables by branched continued fractions, in particular, multidimensional A- and J-fractions with independent variables. A generalization of Gragg's algorithm is…

We define, and obtain the meromorphic continuation of, shifted Rankin-Selberg convolutions in one and two variables. As sample applications, this continuation is used to obtain estimates for single and double shifted sums and a Burgess-type…

We compute the nonlinearity of Boolean functions with Groebner basis techniques, providing two algorithms: one over the binary field and the other over the rationals. We also estimate their complexity. Then we show how to improve our…

We compute the regulator of Beilinson-Deninger-Scholl elements in terms of special values of L-functions of modular forms, using the Rogers-Zudilin method.

We study characteristic classes on hyperk\"ahler manifolds with a view towards the Verbitsky component. The case of the second Chern class leads to a conditional upper bound on the second Betti number in terms of the Riemann--Roch…

In our previous paper math.QA/0412192 the Cayley-Hamilton identity for the GL(m|n) type quantum matrix algebra was obtained. Here we continue investigation of that identity. We derive it in three alternative forms and, most importantly, we…

A symmetric function of $N$ variables can be given in terms of symmetric polynomials of these variables. We determine those symmetric polynomials in which the dual differential operators take the neatest form when expressed in terms of our…

We discuss secondary (and higher) characteristic classes for algebraic vector bundles with trivial top Chern class. We show that if X is a smooth affine scheme of dimension d over a field k of finite 2-cohomological dimension (with char(k)…

We show that Quillen's formalism for computing the Chern character of the index using superconnections extends to arbitrary operators with functional calculus. We thus remove the condition that the operators have, up to homotopy, a gap in…

We obtain refined generating series formulae for equivariant characteristic classes of external and symmetric products of singular complex quasi-projective varieties. More concretely, we study equivariant versions of Todd, Chern and…

We prove an explicit formula for the Bergman kernel of polarized abelian varieties. As applications, we show that if two positive line bundles represent the same first Chern class and have identical Bergman kernel functions for some tensor…

We establish a general computational scheme designed for a systematic computation of characteristic classes of singular complex algebraic varieties that satisfy a Gysin axiom in a transverse setup. This scheme is explicitly geometric and of…