Related papers: A Monomial Basis for the Holomorphic Functions on …

The purpose of this paper is to prove the long awaited holomorphy of the third symmetric power L-functions attached to nonmonomial cusp forms of GL_2 over an arbitrary number field on the whole complex plane.

An old theorem of Weil and Kodaira says that for a compact K\"ahler manifold $X$ there is a closed logarithmic $1$-form with residue divisor $D$ if and only if $D$ is homologous to zero in $H_{2n-2}(X,\mathbb C)$. In the first part of this…

Let $(\Omega, \mu)$ be a probability space endowed with an ergodic action, $\tau$ of $( {\mathbb R} ^n, +)$. Let $H(x,p; \omega)=H_\omega(x,p)$ be a smooth Hamiltonian on $T^* {\mathbb R} ^n$ parametrized by $\omega\in \Omega$ and such that…

The present paper is a continuation of our work [11], where we introduced a fractional operator calculus related to a fractional ${\psi}-$Fueter operator in the one-dimensional Riemann-Liouville derivative sense in each direction of the…

Let $G$ be a simply connected exponential solvable Lie group, $H$ a closed connected subgroup, and let $\tau$ be a representation of $G$ induced from a unitary character $\chi_f$ of $H$. The spectrum of $\tau$ corresponds via the orbit…

In this paper, we prove that unital homomorphisms from continuous functions on a compact metric space to matrices over a C*-algebra with tracial rank at most one are approximately diagonalizable. We also consider some generalizations of…

We produce a cofibrantly generated simplicial symmetric monoidal model structure for the category of (small unital) C*-categories, whose weak equivalences are the unitary equivalences. The closed monoidal structure consists of the maximal…

We investigate the affine canonical basis and the monomial basis constructed in [LXZ] in Lusztig's geometric setting. We show that the transition matrix between the two bases is upper triangular with 1's in the diagonal and coefficients in…

We provide explicit formulas for the orthogonal eigenfunctions of the supersymmetric extension of the rational Calogero-Moser-Sutherland model with harmonic confinement, i.e., the generalized Hermite (or Hi-Jack) polynomials in superspace.…

A basis of Lorentz and gauge-invariant monomials in non--Abelian gauge theories with matter is described, applicable for the inverse mass expansion of effective actions. An algorithm to convert an arbitrarily given invariant expression into…

Garsia-Haiman modules are quotient rings in variables X_n={x_1, x_2, ..., x_n} and Y_n=y_1, y_2, ..., y_n} that generalize the quotient ring C[X_n]/I, where I is the ideal generated by the elementary symmetric polynomials e_j(X_n) for 1 <=…

We prove divisibility results for the Fourier coefficients of canonical basis elements for the spaces of weakly holomorphic modular forms of weight $0$ and levels $6, 10, 12, 18$ with poles only at the cusp at infinity. In addition, we show…

The isomonodromic tau function of the Fuchsian differential equations associated to Frobenius structures on Hurwitz spaces can be viewed as a section of a line bundle on the space of admissible covers. We study the asymptotic behavior of…

We describe a recursive algorithm that produces an integral basis for the centre of the Hecke algebra of type A consisting of linear combinations of monomial symmetric polynomials of Jucys--Murphy elements. We also discuss the existence of…

We study cohomology with coefficients in a rank one local system on the complement of an arrangement of hyperplanes $\A$. The cohomology plays an important role for the theory of generalized hypergeometric functions. We combine several…

In this paper, we investigate the evaluation problem of the Haar state on the quantum group $O(U_q(n))$ ($n\ge 3$) which is a $q$-deformation of the Haar measure on the Lie group $U(n)$. The relation between the Haar state values of…

We construct bases of polynomials for the spaces of square-integrable harmonic functions which are orthogonal to the monogenic and antimonogenic $\mathbb{R}^3$-valued functions defined in a prolate or oblate spheroid.

We introduce a metric-dependent geometric variant of factorization homology in conformally flat Riemannian geometry for $d \geq 2$. Its coefficients are symmetric monoidal functors from a disk category in conformal Riemannian geometry to…

Let $X_\lambda$ and $X_\lambda'$ be monomial deformations of two Delsarte hypersurfaces in weighted projective spaces. In this paper we give a sufficient condition so that their zeta functions have a common factor. This generalises results…

We give an explicit construction of Haar functions associated to a system of dyadic cubes in a geometrically doubling quasi-metric space equipped with a positive Borel measure, and show that these Haar functions form a basis for $L^p$. Next…