Related papers: Unitary Representations and Theta Correspondence f…

We survey a research program on the strong convergence of unitary and permutation representations of discrete groups. We also take the opportunity to flesh out details that have not appeared elsewhere.

If every point of a unital is fixed by a non-trivial translation and at least one translation has order two then the unital is classical (i.e., hermitian).

We find identities between theta constants with rational characteristics evaluated at period matrix of $R,$ a cyclic 3 sheeted cover of the sphere with $3k$ branch points $\lambda_1...\lambda_{3k}.$ These identities follow from Thomae…

Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…

A modular fusion category C allows one to define projective representations of the mapping class groups of closed surfaces of any genus. We show that if all these representations are irreducible, then C has a unique Morita-class of simple…

This thesis is devoted to the study of the interactions existing between the algebraic structure of locally compact groups and the properties of their continuous unitary representations, with a special emphasis on the Type I groups. On the…

We describe the construction and properties of a singular theta lift for the orthogonal group $\SO(2,1)$. We obtain locally harmonic Maass forms in the sense of Bringmann-Kane-Kohnen with singular sets along geodesics in the upper half…

We describe those group algebras over fields of characteristic different from 2 whose units symmetric with respect to the classical involution, satisfy some group identity.

In this article we introduce order preserving representations of fundamental groups of surfaces into Lie groups with bi-invariant orders. By relating order preserving representations to weakly maximal representations, introduced in…

Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of fundamental decision problems. A particular focus of research has been the…

We provide a practical technique to obtain plenty of algebraic relations for theta functions on the bounded symmetric domains of type $I$. In our framework, each theta relation is controlled by combinatorial properties of a pair $(T,P)$ of…

In this short survey article, we try to list maximum number of known results on class preserving automorphisms of finite $p$-groups. We conclude the survey with some interesting (at least for the author) open problems on this topic.

Simple argument in favour of unitarity, to all orders, of space-like noncommutative theory is given.

There are many generalizations of the McKay correspondence for higher dimensional Gorenstein quotient singularities and there are some applications to compute the topological invariants today. But some of the invariants are completely…

In this paper, we propose a new conjecture describing the structure of the unitary dual in terms of Arthur representations for connected reductive algebraic groups defined over any non-Archimedean local field of characteristic zero. This…

Our aim is to describe the theory of Cartesian decompositions preserved by some member of a large family of finite transitive permutation groups called innatelytransitive groups.

We show that the Union-Closed Conjecture holds for the union-closed family generated by the cyclic translates of any fixed set.

We propose a generalisation of the Jacquet-Langlands correspondence to the whole Grothendieck group of finite lenght admissible representations. As an application we prove some particular cases of the global Jacquet-Langlands…

The Langlands correspondence of GL(2,F) over a non-Archimedean local field F of characteristic 0 has been well studied. The construction uses the theta correspondence. In this paper, we are going to describe explicitly how this construction…

Based on a recent result of Mathas and the author, we prove that Uno's conjecture on representation types of Hecke algebras is true for all Hecke algebras of classical type.