Related papers: Theta Correspondence and Quantum Induction

An "automatic continuity" question has naturally occurred since Roger Howe established the local theta correspondence over $\mathbb R$: does the algebraic version of local theta correspondence over $\mathbb R$ agrees with the smooth…

The relationship that is widely presumed to hold between physical theories and their successors, in which the successors in some sense explain the success of the theories they replace, is known commonly as 'reduction.' I argue that one…

We work in the Heisenberg picture to demonstrate the classical-quantum correspondence (CQC) in which the dynamics of a quantum variable is equivalent to that of a complexified classical variable. The correspondence provides a tool for…

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…

Let $(G,G')$ be a reductive dual pair of a symplectic group and an orthogonal group over a finite field of odd characteristic. The Howe correspondence establishes a correspondence between a subset of irreducible characters of $G$ and a…

Communication in a network generally takes place through a sequence of intermediate nodes connected by communication channels. In the standard theory of communication, it is assumed that the communication network is embedded in a classical…

In a companion paper (hereafter referred to as Paper I), we have presented an attempt to derive the finite-dimensional abstract quantum formalism within the framework of information geometry. In this paper, we formulate a correspondence…

We give a proof of the Howe duality conjecture in local theta correspondence for symplectic-orthogonal or unitary dual pairs in arbitrary residual characteristic.

S.-Y. Pan decomposes the uniform projection of the Weil representation of a finite symplectic-odd orthogonal dual pair, in terms of Deligne-Lusztig virtual characters, assuming that the order of the finite field is large enough. In this…

Let (G,H) be one of the equal rank reductive dual pairs (Mp_{2n},O_{2n+1}) or (U_n,U_n) over a non-archimedean local field of characteristic zero. It is well-known that the theta correspondence establishes a bijection between certain…

We present an application of Hodge theory towards the study of irreducible unitary representations of reductive Lie groups. We describe a conjecture about such representations and discuss some progress towards its proof.

We prove that the well-known explicit construction of the local theta correspondence by Li has a simple interpretation in terms of group C*-algebras. In particular, we deduce that in two standard cases where Li's method work, local theta…

Geometric/arithmetic theta correspondences provide correspondences between automorphic forms and cohomology classes/algebraic cycles on Shimura varieties. We give an introduction focusing on the example of unitary groups and highlight…

Quantum-classical correspondence in conservative chaotic Hamiltonian systems is examined using a uniform structure measure for quantal and classical phase space distribution functions. The similarities and differences between quantum and…

We introduce the construction of induced corepresentations in the setting of locally compact quantum groups and prove that the resulting induced corepresentations are unitary under some mild integrability condition. We also establish a…

In a companion paper (hereafter referred to as Paper I), we have presented an attempt to derive the finite-dimensional abstract quantum formalism from a set of physically comprehensible assumptions. In this paper, we formulate a…

Using theta correspondence, we obtain a classification of irreducible representations of an arbitrary even orthogonal group (i.e. the local Langlands correspondence) by deducing it from the local Langlands correspondence for symplectic…

The correspondence principle plays an important role in understanding the emergence of classical chaos from an underlying quantum mechanics. Here we present an infinite family of quantum dynamics that never resembles the analogous classical…

We numerically study the work distributions in a chaotic system and examine the relationship between quantum work and classical work. Our numerical results suggest that there exists a correspondence principle between quantum and classical…

In the 1940s Littlewood formulated three fundamental correspondences for the immanants and Schur symmetric functions on the general linear group, which establish deep connections between representation theory of the symmetric group and the…