The Dual Pair PGL3 × G2

1997 ◽  
Vol 40 (3) ◽  
pp. 376-384
Author(s):  
Benedict H. Gross ◽  
Gordan Savin
Keyword(s):  
Closed Subgroup ◽  
Dual Pair ◽  
Adjoint Group ◽  
Minimal Representation

AbstractLet H be the split, adjoint group of type E6 over a p-adic field. In this paper we study the restriction of the minimal representation of H to the closed subgroup PGL3 × G2.

A Class of Supercuspidal Representations of G2(k)

1999 ◽  
Vol 42 (3) ◽  
pp. 393-400 ◽  
Author(s):  
Gordan Savin
Keyword(s):  
Division Algebra ◽  
Dual Pair ◽  
Adjoint Group ◽  
Minimal Representation ◽  
Supercuspidal Representations ◽  
Interesting Class ◽  
Rank 2 ◽  
Split Rank

AbstractLet H be an exceptional, adjoint group of type E6 and split rank 2, over a p-adic field k. In this article we discuss the restriction of the minimal representation of H to a dual pair PD× × G2(k), where D is a division algebra of dimension 9 over k. In particular, we discover an interesting class of supercuspidal representations of G2(k).

The Dual Pair G2 × PU3 (D) (p-Adic Case)

1999 ◽  
Vol 51 (1) ◽  
pp. 130-146 ◽  
Author(s):  
Gordan Savin ◽  
Wee Teck Gan
Keyword(s):  
Linear Group ◽  
Main Tool ◽  
Dual Pair ◽  
Parabolic Subgroups ◽  
Minimal Representation ◽  
Relative Rank ◽  
Adic Case ◽  
Maximal Parabolic Subgroups

AbstractWe study the correspondence of representations arising by restricting the minimal representation of the linear group of type E7 and relative rank 4. The main tool is computations of the Jacquet modules of the minimal representation with respect to maximal parabolic subgroups of G2 and PU3(D).

scholarly journals Heisenberg Doubles for Snyder-Type Models

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1055
Author(s):  
Stjepan Meljanac ◽  
Anna Pachoł
Keyword(s):  
Phase Space ◽  
Lie Algebra ◽  
Dual Pair ◽  
One Dimension ◽  
Lorentz Algebra ◽  
Explicit Formulae ◽  
Heisenberg Double

A Snyder model generated by the noncommutative coordinates and Lorentz generators closes a Lie algebra. The application of the Heisenberg double construction is investigated for the Snyder coordinates and momenta generators. This leads to the phase space of the Snyder model. Further, the extended Snyder algebra is constructed by using the Lorentz algebra, in one dimension higher. The dual pair of extended Snyder algebra and extended Snyder group is then formulated. Two Heisenberg doubles are considered, one with the conjugate tensorial momenta and another with the Lorentz matrices. Explicit formulae for all Heisenberg doubles are given.

scholarly journals Constructing weak simulations from linear implications for processes with private names

2019 ◽  
Vol 29 (8) ◽  
pp. 1275-1308 ◽  
Author(s):  
Ross Horne ◽  
Alwen Tiu
Keyword(s):  
Expressive Power ◽  
Dual Pair ◽  
Proof System ◽  
Branching Time ◽  
First Order ◽  
Order Extension

AbstractThis paper clarifies that linear implication defines a branching-time preorder, preserved in all contexts, when used to compare embeddings of process in non-commutative logic. The logic considered is a first-order extension of the proof system BV featuring a de Morgan dual pair of nominal quantifiers, called BV1. An embedding of π-calculus processes as formulae in BV1 is defined, and the soundness of linear implication in BV1 with respect to a notion of weak simulation in the π -calculus is established. A novel contribution of this work is that we generalise the notion of a ‘left proof’ to a class of formulae sufficiently large to compare embeddings of processes, from which simulating execution steps are extracted. We illustrate the expressive power of BV1 by demonstrating that results extend to the internal π -calculus, where privacy of inputs is guaranteed. We also remark that linear implication is strictly finer than any interleaving preorder.

scholarly journals Extending Edgar's ordering to locally convex spaces

1992 ◽  
Vol 34 (2) ◽  
pp. 175-188
Author(s):  
Neill Robertson
Keyword(s):  
Convex Space ◽  
Dual Pair ◽  
Locally Convex Space ◽  
Vector Spaces ◽  
Locally Convex Spaces ◽  
Continuous Linear ◽  
Linear Functionals ◽  
Hausdorff Topological Vector Space ◽  
Locally Convex ◽  
Mackey Topologies

By the term “locally convex space”, we mean a locally convex Hausdorff topological vector space (see [17]). We shall denote the algebraic dual of a locally convex space E by E*, and its topological dual by E′. It is convenient to think of the elements of E as being linear functionals on E′, so that E can be identified with a subspace of E′*. The adjoint of a continuous linear map T:E→F will be denoted by T′:F′→E′. If 〈E, F〈 is a dual pair of vector spaces, then we shall denote the corresponding weak, strong and Mackey topologies on E by α(E, F), β(E, F) and μ(E, F) respectively.

scholarly journals Dual pairs of sequence spaces

2001 ◽  
Vol 28 (1) ◽  
pp. 9-23 ◽  
Author(s):  
Johann Boos ◽  
Toivo Leiger
Keyword(s):  
Sequence Space ◽  
Dual Pair ◽  
General Concept ◽  
Sequence Spaces ◽  
Dual Pairs ◽  
The Third ◽  
Convex Sequence ◽  
Starting Point ◽  
Alpha Beta ◽  
Locally Convex

The paper aims to develop for sequence spacesEa general concept for reconciling certain results, for example inclusion theorems, concerning generalizations of the Köthe-Toeplitz dualsE×(×∈{α,β})combined with dualities(E,G),G⊂E×, and theSAK-property (weak sectional convergence). TakingEβ:={(yk)∈ω:=𝕜ℕ|(ykxk)∈cs}=:Ecs, wherecsdenotes the set of all summable sequences, as a starting point, then we get a general substitute ofEcsby replacingcsby any locally convex sequence spaceSwith sums∈S′(in particular, a sum space) as defined by Ruckle (1970). This idea provides a dual pair(E,ES)of sequence spaces and gives rise for a generalization of the solid topology and for the investigation of the continuity of quasi-matrix maps relative to topologies of the duality(E,Eβ). That research is the basis for general versions of three types of inclusion theorems: two of them are originally due to Bennett and Kalton (1973) and generalized by the authors (see Boos and Leiger (1993 and 1997)), and the third was done by Große-Erdmann (1992). Finally, the generalizations, carried out in this paper, are justified by four applications with results around different kinds of Köthe-Toeplitz duals and related section properties.

Symplectic Dual Pair Related to Deformed SO(5)

2014 ◽  
pp. 121-130
Author(s):  
Alina Dobrogowska ◽  
Anatol Odzijewicz
Keyword(s):  
Dual Pair
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