Related papers: A nonabelian trace formula
We establish the coarse relative trace formulae of Jacquet-Rallis for linear and unitary groups. Both formulae are of the form: a sum of spectral distributions equals a sum of geometric distributions. In order to obtain the spectral…
A scalar model of glueball is considered. The model is based on two scalar fields approximation for SU(3) non-Abelian Lagrangian. The approach to approximation makes use of the assumption that 2 and 4-points Green's functions are described…
We prove that over totally real fields, the $p$-adic Galois representations attached to non-self-dual regular algebraic cuspidal automorphic representations of $\mathrm{GL}(4)$ are irreducible. We then develop the theory of extra-twists in…
In 2018, Legrand and Paran proved a weaker form of the Inverse Galois Problem for all Hilbertian fields and all finite groups: that is, there exist possibly non-Galois extensions over given Hilbertian base field with given finite group as…
For a cuspidal automorphic representation \Pi of GL(4,A), H. Kim proved that the exterior square transfer \wedge^2\Pi is an isobaric automorphic representation of GL(6,A). In this paper we characterize those representations \Pi for which…
An infinite filiform Lie algebra L is residually nilpotent and its graded associated with respect to the lower central series has smallest possible dimension in each degree but is still infinite. This means that gr(L) is of dimension two in…
Let $E/F$ be a quadratic extension of local nonarchimedean fields of characteristic zero and let $D$ be a quaternion algebra over $F$ containing $E$. In this paper, we study a relation between the existence of twisted linear models on…
We consider continuous representations of the Galois group G of a number field K taking values in the completion C of an algebraic closure A of the field of l-adic numbers. We give a construction of irreducible representations of G in…
We present a simple derivation of the one-loop trace anomaly in spinor QED through dispersion relations, avoiding completely any ultraviolet regularization. The anomaly can be expressed as a convergent sum rule for the imaginary part of a…
Using the stable twisted trace formula for the triality automorphism, we show the adjoint lifting (to GL(8)) of cuspidal representations of GL(3) with a discrete series local component. We also describe the possible isobaric decompositions…
This text is based on a talk by the first named author at the first congress of the SMF (Tours, 2016). We present Bloch's conductor formula, which is a conjectural formula describing the change of topology in a family of algebraic varieties…
We study the distribution of the traces of the Frobenius endomorphism of genus $g$ curves which are quartic non-cyclic covers of $\mathbb{P}^{1}_{\mathbb{F}_{q}}$, as the curve varies in an irreducible component of the moduli space. We show…
We study properties of C*-algebraic deformations of homogeneous spaces $G/\Gamma$ which are equivariant in the sense that they preserve the natural action of $G$ by left translation. The center is shown to be isomorphic to $C(G/G_\rho^0)$…
By applying the new supersymmetric localization principle introduced in \cite{Choi:2021yuz,Choi:2023pjn}, we present two complementary approaches for the path integral derivation of the `non-chiral' trace formula for a semisimple compact…
The l-adic parabolic cohomology groups attached to noncongruence subgroups of SL_2(Z) are finite-dimensional representations of Gal(Qbar/F) for some number field F. We exhibit examples (with F=Q) giving rise to Galois representations whose…
In this article, we consider the nonlinear Steklov eigenvalue problem in outward cuspidal domains. Using the compactness of the weighted trace embedding we obtain the variational characterization of the first non-trivial eigenvalue and…
We provide an adelic relative trace formula proof to the Petersson/Bruggeman-Kuznetsov (PBK) formulas, specifically in the holomorphic case for $\kappa=2$ and the non-holomorphic case for $m_1m_2<0$. Given two sets of hypothesis on the non…
Let $q$ be a quadratic form over a field $F$ and let $L$ be a field extension of $F$ of odd degree. It is a classical result that if $q_L$ is isotropic (resp. hyperbolic) then $q$ is isotropic (resp. hyperbolic). In turn, given two…
In this note, using a representation theoretic method of Cogdell and Piatetski-Shapiro, we prove the Kuznetsov trace formula for an arbitrary discrete group $\Gamma$ in $\mathrm{PGL}_2(\mathbb{C})$ that is cofinite but not cocompact. An…
Let $F$ be a CM field with totally real subfield $F^+$ and let $\pi$ be a $C$-algebraic cuspidal automorphic automorphic representation of $\mathrm{U}(a,b)(\mathbf{A}_{F^+})$ whose archimedean components lie in the (non-degenerate limit of)…