Related papers: Some quantitative versions of Ratner's mixing esti…
Recently, by studying an explicit basis, K\"ock and Laurent give the decomposition of the $\overline{\mathbb{F}}_q[\mathrm{SL}_2(\mathbb{F}_q)]$-module of holomorphic forms on the Drinfeld curve. We present a crystalline cohomological proof…
We determine the characters of SL(2) representations of groups and surface groups.
QED radiative corrections to polarized muon decay spectrum are considered. Leading and next--to--leading logarithmic approximations are used. Exponentiation of soft radiation is discussed. The present theoretical uncertainty of the spectrum…
We present integral representations of solutions to division problems involving matrices of polynomials in several complex variables. We also find estimates of the polynomial degree of the solutions by means of careful degree estimates of…
Simple deformations, with a parameter $\epsilon$, of classical $R$-matrices which follow from decomposition of appropriate Lie algebras, are considered. As a result nonstandard Lax representations for some well known integrable systems are…
We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…
In this note we present a complete analysis of finite dimensional representations of the Lie superalgebra sl(2|1). This includes, in particular, the decomposition of all tensor products into their indecomposable building blocks. Our…
We describe our conjecture about the irreducible unitary representations of reductive Lie groups, in the special case of $\mathrm{SL}(2,\mathbb{R})$.
In this work, new closed-form formulas for the matrix exponential are provided. Our method is direct and elementary, it gives tractable and manageable formulas not current in the extensive literature on this essential subject. Moreover,…
The status of lattice calculations of heavy quark phenomenology is reviewed. Particular emphasis is placed on the understanding and control of the calculational uncertainties. The ensuing implications for constraining the CKM matrix…
This paper gives a brief review on the recent lattice QCD calculations of the B to K/K*l+l- semi-leptonic decay form factors.
We present and compare several algorithms for evaluating Jacquet's Whittaker functions for SL(3, Z). The most suitable algorithm is then applied to the problem of evaluating a Maass form for SL(3, Z) with known eigenvalues and Fourier…
Under suitable hypotheses on the ground field and on the matrix $M$, we discuss existence, uniqueness and properties of some additive decompositions of $M$ and of its image through a convergent series.
Cayley rational forms for rotations are given as explicit spin matrix polynomials for any j. The results are compared to the Curtright-Fairlie-Zachos matrix polynomials for rotations represented as exponentials.
Consider the Fourier transform on the group $GL(2,R)$ of real $2\times 2$-matrices. We show that Fourier-images of polynomial differential operators on $GL(2,R)$ are differential-difference operators with coefficients meromorphic in…
We determine the graded decompositions of fusion products of finite-dimensional irreducible representations for simple Lie algebras of rank two. Moreover, we give generators and relations for these representations and obtain as a…
We exploit the truncated singular value decomposition and the recently proposed circulant decomposition for an efficient first-order approximation of the multiplication of large dense matrices. A decomposition of each matrix into a sum of a…
We obtain an explicit integral representation of Siegel-Whittaker functions on Sp(2,R) for the large discrete series representations. We have another integral expression different from that of Miyazaki [7].
Novel relativistic expressions are used to calculate the weak decay constants of pseudoscalar and vector mesons within the constituent quark model. Meson wave functions satisfy the quasipotential equation with the complete relativistic…
The status of lattice calculations of some phenomenology of heavy quarks is presented. Emphasis is on progress made in calculating those quantities relevant to estimating parameters of the quark mixing matrix, namely leptonic decay…