Related papers: Stein--Sahi complementary series and their degener…

In our earlier article~\cite{CanSakran} we initiated a study of the complement-finite submonoids of the group of integer points of a unipotent linear algebraic group. In the present article, we continue to develop tools and techniques for…

Let $U$ be an algebraic subgroup of the group of $n\times n$ upper-triangular matrices with units on the diagonal over a finite field of large enough characteristic, and $\mathfrak{n}$ be the Lie algebra of $U$. The main tool in…

At first a type of Eisenstein series is defined as distributions giving nearly-holomorphic automorphic forms on a totally real field, with different expressions (integral, summation) ; then these are shown to satisfied the expected…

We study the restrictions of certain degenerate principal series representations of the universal covering of the symplectic group. We construct an isometry between the complementary series and the unitary principal series which preserves…

With this work we initiate a study of the representations of a unipotent group over a field of characteristic zero from the modular point of view. Let $G$ be such a group. The stack of all representations of a fixed finite dimension $n$ is…

We identify a class of "semi-modular" forms invariant on special subgroups of $GL_2(\mathbb Z)$, which includes classical modular forms together with complementary classes of functions that are also nice in a specific sense. We define an…

In this note we consider representations of the group GL(n,F), where F is the field of real or complex numbers or, more generally, an arbitrary local field, in the space of equivariant line bundles over Grassmannians over the same field F.…

The Eulerian idempotents, first introduced for the symmetric group and later extended to all reflection groups, generate a family of representations called the Eulerian representations that decompose the regular representation. In Type $A$,…

In this paper we study the reducibility, composition series and unitarity of the components of some degenerate principal series representations of $\RMO(p,q)$, $\RMU(p,q)$ and $\SP(p,q)$. This is done by realizing these representations in…

We determine the unipotent orbits attached to degenerate Eisenstein series on general linear groups. This confirms a conjecture of David Ginzburg. This also shows that any unipotent orbit of general linear groups does occur as the unipotent…

This paper is an attempt to apply the tools of supergeometry to arithmetic. Supergeometric objects are defined over supercommutative rings of coefficients, and we consider an integral ring with exactly two odd variables. In this case the…

We first review some invariant theoretic results about the finite subgroups of SU(2) in a quick algebraic way by using the McKay correspondence and quantum affine Cartan matrices. By the way it turns out that some parameters (a,b,h;p,q,r)…

We discuss one natural class of kernels on pseudo-Riemannian symmetric spaces.

This paper studies unitary representations with Dirac cohomology for complex groups, in particular relations to unipotent representations

We analyze the elements characterizing the theory of induced representations of Lie groups, in order to generalize it to quantum groups. We emphasize the geometric and algebraic aspects of the theory, because they are more suitable for…

In this paper we study a quantum analogue of a degenerate principal series of $U_q \mathfrak{su}_{n,n}$-modules ($0<q<1$) related to the Shilov boundary of the quantum $n \times n$-matrix unit ball. We give necessary and sufficient…

These notes contain an introduction to the theory of complex semisimple quantum groups. Our main aim is to discuss the classification of irreducible Harish-Chandra modules for these quantum groups, following Joseph and Letzter. Along the…

We study triples of graded rings defined over the deformation spaces for certain one-parameter families of Calabi-Yau threefolds. These rings are analogues of the rings of modular forms, quasi-modular forms and almost-holomorphic modular…

We study a family of complex representations of the group GL(n,O), where O is the ring of integers of a non-archimedean local field F. These representations occur in the restriction of the Grassmann representation of GL(n,F) to its maximal…

Faithful representations of regular $\ast$-rings and modular complemented lattices with involution within orthosymmetric sesquilinear spaces are studied within the framework of Universal Algebra. In particular, the correspondence between…