Related papers: Linear Independence for $A_1^{(1)}$ by Using $C_{2…

We develop a new method for proving algebraic independence of $G$-functions. Our approach rests on the following observation: $G$-functions do not always come with a single linear differential equation, but also sometimes with an infinite…

We develop a minimal and fully anomaly-free realization of a universal leptophilic $U(1)'_{\ell}$ gauge symmetry, under which all Standard-Model leptons carry a common charge while quarks remain neutral. Gauge consistency is restored by…

We give new combinatorial formulas for decomposition of the tensor product of integrable highest weight modules over the classical Lie algebras of type $B, C, D$, and the branching decomposition of an integrable highest weight module with…

We classify simple Whittaker modules for classical Lie superalgebras in terms of their parabolic decompositions. We establish a type of Mili\v{c}i\'c-Soergel equivalence of a category of Whittaker modules and a category of Harish-Chandra…

It is an open question of Baker whether the numbers $L(1, \chi)$ for non-trivial Dirichlet characters $\chi$ with period $q$ are linearly independent over $\mathbb{Q}$. The best known result is due to Baker, Birch and Wirsing which affirms…

In this paper we develop a general method to prove independence of algebraic monodromy groups in compatible systems of representations, and we apply it to deduce independence results for compatible systems both in automorphic and in…

We give a simple combinatorial proof of the $\lambda_g$ conjectue in genus 2. We use a description of the class $\lambda_2$ as a linear combination of boundary strata, and show the conjecture follows inductively from applications of the…

Let $\mathfrak g$ be a complex semisimple Lie algebra. We define what it means for a finite dimensional representation of $\mathfrak g$ to be rectangular and completely classify faithful rectangular representations. As an application, we…

We prove a T(1) theorem for bilinear singular integral operators (trilinear forms) with a one-dimensional modulation symmetry.

Let $\mathcal{M}$ be a $W^*$-factor and let $S\left( \mathcal{M} \right) $ be the space of all measurable operators affiliated with $\mathcal{M}$. It is shown that for any self-adjoint element $a\in S(\mathcal{M})$ there exists a scalar…

We study the canonical structure of the $SU(N)$ non-linear Sigma-model in a polynomial, first-order representation. The fundamental variables in this description are a non-Abelian vector field L_mu and a non-Abelian antisymmetric tensor…

Linear forms in logarithms over connected commutative algebraic groups over the algebraic numbers field have been studied widely. However, the theory of linear forms in logarithms over noncommutative algebraic groups have not been developed…

Two known results on the relationship between conditional and unconditional independence are obtained as a consequence of the main result of this paper, a theorem that uses independence of Markov kernels to obtain a minimal condition which…

We show that if a module M over a basic classical Lie superalgebra of type type I is simultaneously a Verma module with respect to some Borel \(\mathfrak b_1\) and a dual Verma module with respect to Borel \(\mathfrak b_2\), then M is…

Let $s\colon X\rightarrow \operatorname{Spec} \mathbb{F}$ be a separated scheme of finite type over a finite field $\mathbb{F}$ of characteristic $p$, let $\Lambda$ be a not necessarily commutative $\mathbb{Z}_p$-algebra with finitely many…

This thesis is devoted to the study of joint spectral multipliers for a system of pairwise commuting, self-adjoint left-invariant differential operators L_1,...,L_n on a connected Lie group G. Under the assumption that the algebra generated…

This paper aims to undertake an exploration of the behavior of the moduli space of line arrangements while establishing its combinatorial interplay with the incidence structure of the arrangement. In the first part, we investigate…

In this work, the null controllability problem for a linear system in $\ell^2$ is considered, where the matrix of a linear operator describing the system is an infinite matrix with $\lambda\in \mathbb R$ on the main diagonal and 1s above…

We use an effective matrix model to study deconfinement in a pure SU(Nc) gauge theory, without quarks, in d=2+1 dimensions. Expanding about a constant background A0 field we construct an effective potential for the eigenvalues of the…

In [B-G1] and [B-G2], Borisov and Gunnells constructed for each level (N > 1) and for each weight (k > 1) a modular symbol with values in $Sk(\Gamma_1(N))$ using products of Eisenstein series. In this paper we generalize this result by…