Related papers: Composition series of a class of induced represent…
This is Part IV of a thematic series currently consisting of a monograph and four essays. This essay examines the form of induced representations of locally p-adic Lie groups G which is appropriate for the abelian category of ${\mathcal…
We explicitly construct the structure of Jacquet modules of parabolically induced representations of even unitary groups and even general unitary groups over a $p$-adic field $F$ of characteristic different than two. As an application, we…
By work of De Concini, Kac and Procesi the irreducible representations of the non-restricted specialization of the quantized enveloping algebra of the Lie algebra g at the roots of unity are parametrized by the conjugacy classes of a group…
We study representations of segment type of groups Sp(n) and SO(2n+1, F) over a local non-archimedean field, which play a fundamental role in the constructions of discrete series, and obtain a complete description of the Jacquet modules of…
Utilizing spectral residues of parameterized, recursively defined sequences, we develop a general method for generating identities of composition sums. Specific results are obtained by focusing on coefficient sequences of solutions of first…
In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…
In this paper, we give a construction of the moduli space of filtered representations of a given quiver of fixed dimension vector with the appropriate notion of stability. The construction of the moduli of filtered representations uses the…
We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…
Presented is a novel methodology for determining representational structure, which builds upon the existing Spotlight Resonance method. This new tool is used to gain insight into how discrete representations can emerge and organise in…
Making use of a unified approach to certain classes of induced representations, we establish here a number of detailed spectral theoretic decomposition results. They apply to specific problems from non-commutative harmonic analysis, ergodic…
We introduce a class of ${\mathbb{Z}}_N$ graded discrete Lax pairs, with $N\times N$ matrices, linear in the spectral parameter. We give a classification scheme for such Lax pairs and the associated discrete integrable systems. We present…
In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…
We study the theta lifting for real unitary groups and completely determine the theta lifts of discrete series representations. In particular, we show that these theta lifts can be expressed as cohomologically induced representations in the…
We use the theta correspondence to study the equivalence between Godement-Jacquet and Jacquet-Langlands L-functions for $\mathrm{GL}(2)$. We show that the resulting comparison is in fact an exotic symmetric monoidal structure on the…
We introduce two classes of discrete polynomials and construct discrete equations admitting a Lax representation in terms of these polynomials. Also we give an approach which allows to construct lattice integrable hierarchies in its…
The paper proposes a novel technique for representing templates and instances of concept classes. A template representation refers to the generic representation that captures the characteristics of an entire class. The proposed technique…
In this paper we study n-composition series of affine manifolds. One composition series are classified using gerbe theory. It is natural to think that n-composition series must be classified using n-gerbe theory. In the last section of…
The goal of this paper is to prove how Arthur's results, in the case of split odd orthogonal p-adic groups, imply the Langlands' classification of discrete series. Of course this need the validity of ''fundamental'' lemmas which are not yet…
On classes of functions defined on R^2n we introduce abstract composition laws modelled after the pseudodifferential product of symbols. We attach to these composition laws modulation mappings and spaces with useful algebraic and…
This paper has two aims. The first is to give a description of irreducible tempered representations of classical p-adic groups which follows naturally the classification of irreducible square integrable representations modulo cuspidal data…