Related papers: Global long root $A$-packets for $\mathsf{G}_2$: t…

We prove the existence of GSpin-valued Galois representations corresponding to cohomological cuspidal automorphic representations of general symplectic groups over totally real number fields under the local hypothesis that there is a…

We define the space of nearly holomorphic automorphic forms on a connected reductive group $G$ over $\mathbb{Q}$ such that the homogeneous space $G(\mathbb{R})^1/ K_\infty^\circ$ is a Hermitian symmetric space. By Pitale, Saha and Schmidt's…

Starting with an operator in the universal enveloping algebra of a semi-simple, complex Lie group the nearest neighbor statistics of the spectra of this operator along a sequence of representations are discussed. After a short introduction…

Given a spherical variety X for a group G over a non-archimedean local field k, the Plancherel decomposition for L^2(X) should be related to "distinguished" Arthur parameters into a dual group closely related to that defined by Gaitsgory…

We obtain correction terms to the large N asymptotic expansions of the eigenvalue density for the Gaussian unitary and Laguerre unitary ensembles of random N by N matrices, both in the bulk of the spectrum and near the spectral edge. This…

We construct a family of maximal commutative subalgebras in the tensor product of n copies of the universal enveloping algebra U(g) of a semisimple Lie algebra g. This family is parameterized by collections \mu; z_1,...,z_n, where \mu \in…

In this paper we express certain multiplicities in modular representation-theoretic categories of type A in terms of affine p-Kazhdan-Lusztig polynomials. The representation-theoretic categories we deal with include the categories of…

This paper is concerned with a compatible family of 4-dimensional \ell-adic representations \rho_{\ell} of G_\Q:=\Gal(\bar \Q/\Q) attached to the space of weight 3 cuspforms S_3 (\Gamma) on a noncongruence subgroup \Gamma \subset \SL. For…

For a globally generic cuspidal automorphic representation $\mathit{\Pi}$ of a quasi-split reductive group $G$ over $\mathbb Q$, E. Lapid and Z. Mao proposed a conjecture on the decomposition of the global Whittaker functionals on…

This paper investigates the cuspidal spectrum of the quotient of the real Lie group $G= SU(n,1)$ and a principal congruence subgroup $\Gamma(m)$ for $m\geq 3$, focusing on the multiplicities of integrable discrete series representations.…

We carry out some algebraic and analytic properties of a new class of orthogonal polyanalytic polynomials, including their operational formulas, recurrence relations, generating functions, integral representations and different…

We consider the holographic duality between type-A higher-spin gravity in AdS_4 and the free U(N) vector model. In the bulk, linearized solutions can be translated into twistor functions via the Penrose transform. We propose a holographic…

We prove that the local eigenvalue statistics of real symmetric Wigner-type matrices near the cusp points of the eigenvalue density are universal. Together with the companion paper [arXiv:1809.03971], which proves the same result for the…

We derive a formula for the global gravitational anomaly of the self-dual field theory on an arbitrary compact oriented Riemannian manifold. Along the way, we uncover interesting links between the theory of determinant line bundles of Dirac…

Let $F/k$ be a cyclic extension of number fields of prime degree. Let $\rho$ be an irreducible $2$-dimensional representation of Artin type of the absolute Galois group of $F$, and $\pi$ a cuspidal automorphic representation of…

Following the approach of B. Roberts, we characterize the non-vanishing of global theta lifts for symplectic-orthogonal dual pairs in terms of its local counterpart. In particular, we replace the temperedness assumption present in Robert's…

We consider tensor-multiscalar representations for several types of modified gravity actions. The first example is the theory with the action representing an arbitrary smooth function of the scalar curvature R and (Box R), the integrand of…

A method to construct in explicit form the generators of the simple roots of an arbitrary finite-dimensional representation of a quantum or standard semisimple algebra is found. The method is based on general results from the global theory…

Isolating cuspidal automorphic representations from the whole automorphic spectrum is a basic problem in the trace formula approach. For example, matrix coefficients of supercupidal representations can be used as test functions for this,…

In the framework of algebraic quantum field theory we analyze the anomalous statistics exhibited by a class of automorphisms of the observable algebra of the two-dimensional free massive Dirac field, constructed by fermionic gauge group…