Related papers: Sato Grassmannian and Degenerate Sigma Function
We show sharp square function estimates for curves in the plane whose curvature degenerates at a point and estimates sharp up to endpoints for cones over these curves. To this end, for curves of finite type we extend the classical…
A telescopic curve is a certain algebraic curve defined by $m-1$ equations in the affine space of dimension $m$, which can be a hyperelliptic curve and an $(n,s)$ curve as a special case. We extend the addition formulae for sigma functions…
We construct the general solution of a class of Fuchsian systems of rank $N$ as well as the associated isomonodromic tau functions in terms of semi-degenerate conformal blocks of $W_N$-algebra with central charge $c=N-1$. The simplest…
We obtain several structure results for a class of spherical subgroups of connected reductive complex algebraic groups that extends the class of strongly solvable spherical subgroups. Based on these results, we construct certain…
Working in the Palatini formalism, we describe a procedure for constructing degenerate solutions of general relativity on 4-manifold M from certain solutions of 2-dimensional BF theory on any framed surface Sigma embedded in M. In these…
This is the first paper in a series where we study arithmetic applications of the multiple elliptic Gamma functions originated from mathematical physics. The main purpose of this paper is the introduction of a framework for applications of…
The decompositions of an element of a finite von Neumann algebra into the sum of a normal operator plus an s.o.t.-quasinilpotent operator, obtained using the Haagerup--Schultz hyperinvariant projections, behave well with respect to…
In case there are tensor interactions beyond the SM in the low-energy effective Lagrangian, their interference with the SM V-A currents yields a contribution for tau decays into three or more mesons that cannot be included in the famous…
The present paper is devoted to studying of some weighted H\"older spaces. These spaces are designed in the way to serve as a framework for studying different statements for the thin film equations in weighted classes of smooth functions in…
We introduce iterated sequences for Grassmannians, a new class of Fang-Fourier-Littelmanns' birational sequences and explain how they give rise to points in $\text{trop}(\text{Gr}(k,\mathbb C^n))$, Speyer-Sturmfels' tropical Grassmannian.…
Let G be any of the complex classical groups GL(n), SO(2n+1), Sp(2n), O(2n), let g denote the Lie algebra of G, and let Z(g) denote the subalgebra of G-invariants in the universal enveloping algebra U(g). We derive a Taylor-type expansion…
This note develops an explicit construction of the constrained KP hierarchy within the Sato Grassmannian framework. Useful relations are established between the kernel elements of the underlying ordinary differential operator and the…
In this paper we define and study a Dedekind-like zeta function for the algebra of multicomplex numbers. By using the idempotent representations for such numbers, we are able to identify this zeta function with the one associated to a…
The monodromy map for a rank-two system of differential equations with three Fuchsian singularities is classically solved by the Kummer formul\ae\ for Gauss' hypergeometric functions. We define the tau-function of such a system as the…
The goal of this paper is to propose a new way to generalize the Weierstrass sigma-function to higher genus Riemann surfaces. Our definition of the odd higher genus sigma-function is based on a generalization of the classical representation…
The differential systems satisfied by orthogonal polynomials with arbitrary semiclassical measures supported on contours in the complex plane are derived, as well as the compatible systems of deformation equations obtained from varying such…
The purpose of this article is to give an explicit description, in terms of hypergeometric functions over finite fields, of zeta function of a certain type of smooth hypersurfaces that generalizes Dwork family. The point here is that we…
This paper deals with some simple results about spherical functions of type $\delta$, namely new integral formulas, new results about behavior at infinity and some facts about the related $C_\sigma$ functions.
For a tau-function of the KP or BKP hierarchy, we introduce the notion of lifting operator and derive an equation connecting the corresponding fermionic two-point function and fermionic one-point function through the lifting operator. This…
We propose a novel approach for studying rooted trees by using functions that we will call descent functions. We provide a construction method for rooted trees that allows to study their properties through the use of descent functions.…