Related papers: Big Theta equals small theta generically

Let $k$ be an algebraically closed field. It is known that any stable equivalence between standard representation-finite self-injective $k$-algebras (without block of Loewy length 2) lifts to a standard derived equivalence, in particular,…

I suggest that the current situation in quantum field theory (QFT) provides some reason to question the universal validity of ontological reductionism. I argue that the renormalization group flow is reversible except at fixed points, which…

In this article, we give a new method for proving Howe correspondence in the case of dual pairs of type $({\rm GL}_n, {\rm GL}_m)$ over a non-Archimedean locally compact field $F$. The proof consists in combining a study on Kudla's…

We study the generalized theta lifting between the double covers of split special orthogonal groups, which uses the non-minimal theta representations constructed by Bump, Friedberg and Ginzburg. We focus on the theta liftings of non-generic…

Lifting theorems form an important collection of tools in showing that Galois representations are associated to automorphic forms. (Key examples in dimension n>2 are the lifting theorems of Clozel, Harris and Taylor and of Geraghty.) All…

In the context of the recent interest in solvable models of scattering mediated by non-Hermitian Hamiltonians (cf. H. F. Jones, Phys. Rev. D 76, 125003 (2007)) we show that and how the well known variability of our ad hoc choice of the…

Let $K[HK_{\Theta}]$ denote the Hecke-Kiselman algebra of a finite oriented graph $\Theta$ over an algebraically closed field $K$. All irreducible representations, and the corresponding maximal ideals of $K[HK_{\Theta}]$, are characterized…

Let $F$ be a non-Archimedean local field. Let $\Cal W_F$ be the Weil group of $F$ and $\Cal P_F$ the wild inertia subgroup of $\scr W_F$. Let $\hat{\Cal W}_F$ be the set of equivalence classes of irreducible smooth representations of $\Cal…

Let $F$ be a locally compact non-Archimedean field, and let $B/F$ be a division algebra of dimension 4. The Jacquet-Langlands correspondence provides a bijection between smooth irreducible representations of $B^\times$ of dimension $>1$ and…

We use relations between the base change representations and theta lifts, to give a new proof to the local period problems of SL(2) over a nonarchimedean quadratic field extension E/F. Then we will verify the Prasad conjecture for SL(2).…

We show that if an irreducible admissible representation of $\mathrm{SO}_{4n}(F)$ has a generalized Shalika model, then its small theta lift to $\mathrm{Sp}_{4n}(F)$ has the symplectic linear model, thus answering a question posed by D.…

We explain how the work of Johnson-Leung and Roberts on lifting Hilbert modular forms for real quadratic fields to Siegel modular forms can be adapted to imaginary quadratic fields. For this we use archimedean results from Harris, Soudry,…

Let $E/L$ be a real quadratic extension of number fields. We construct an explicit map from an irreducible cuspidal automorphic representation of $\mathrm{GL}(2,E)$ which contains a Hilbert modular form with $\Gamma_0$ level to an…

By implementing jet differential techniques in non-archimedean geometry, we obtain a big Picard type extension theorem, which generalizes a previous result of Cherry and Ru. As applications, we establish two hyperbolicity-related results.…

We give a full solution to the question of existence of indiscernibles in dependent theories by proving the following theorem: for every $\theta$ there is a dependent theory $T$ of size $\theta$ such that for all $\kappa$ and $\delta$,…

Let F be a non-archimedean local field. We establish the local Langlands correspondence for all inner forms of the group $SL_n (F)$. It takes the form of a bijection between, on the one hand, conjugacy classes of Langlands parameters for…

We consider sequences of homogeneous sums based on independent random variables and satisfying a central limit theorem (CLT). We address the following question: "In which cases is it not possible to reduce such an asymptotic result to the…

We provide analytical solutions to the thermodynamic Bethe ansatz equations in the large and small density approximations. We extend results previously obtained for leading order behaviour of the scaling function of affine Toda field…

In his paper 'Theta lifting for representations with non zero cohomlogy', Jian-Shu Li proved that a certain kind of cohomological representations of $U(a,b)$ is automorphic. In this paper, this result is generalized to a more general class…

We use the recently introduced \'etale open topology to prove several facts about large fields. We show that these facts lift to a very general topological setting.