Proof of a conjecture of Kudla and Rallis on quotients of degenerate principal series

In this paper we prove a conjecture of Kudla and Rallis. Let $\chi$ be a unitary character, $s\in \mathbb{C}$ and $W$ a symplectic vector space over a non-archimedean field with symmetry group $G(W)$. Denote by $I(\chi,s)$ the degenerate principal series representation of $G(W\oplus W)$. Pulling back $I(\chi,s)$ along the natural embedding $G(W)\times G(W)\hookrightarrow G(W\oplus W)$ gives a representation $I_{W,W}(\chi,s)$ of $G(W)\times G(W)$. Let $\pi$ be an irreducible smooth complex representation of $G(W)$. We then prove $$\dim _\mathbb{C}\mathrm{Hom}_{G(W)\times G(W)}(I_{W,W}(\chi,s),\pi\otimes \pi^\lor)=1.$$ We also give analogous statements for $W$ orthogonal or unitary. This gives in particular a new proof of the conservation relation of the local Theta correspondence for symplectic-orthogonal and unitary dual pairs.Comment: Small corrections being necessitated from a wrong statement in Section

Communities of Practice: An Integrated Technology Perspective

It has been observed that for a Community of Practice (CoP) to be successful, a significant amount of time shall be devoted to understanding the needs of community members. Furthermore, a tool to support the CoP shall be selected based on the kind of activities that are most important for that CoP. Since many of the tools available today place emphasis on a single type of application such as e-learning or document management, unplanned selection may rise unwanted barriers. In this paper, we examine the benefits of integrating some of the following types of technologies into one single technological platform and their impact on CoP: (1) content- and document Management, (2) collaboration / groupware, (3) web conferencing, and (4) e-learning

On the Integration of Formal Methods: Events and Scenarios in PVS and VDM

Tool support is known to be one of the success factors in formal specification based analysis and-program development. This paper investigates tool support in the context of a case study where a wide range of tool features is required: For an access control, C++ code has to be developed based on the user's requirements expressed in natural language. The access control has been classified a mixed data-control problem. This paper discusses (1) why VDMTools and PVS have been selected and (2) how they can be used together. Another aspect is the use of VDM as a framework for modeling event based systems. In our approach to tool integration, two specifications are considered to share a common part. For the present application this part consists of the scenario of all possible events. 1 Introduction 1.1 An Access Control as a Case Study CSS is a security system which has been developed by ARCS (the Austrian Research Center at Seibersdorf [32]). CSS includes features from digital vi..

A Case Study on the Application of PVS to Requirements Analysis

This paper presents the results of a formal methods case study in which the Prototype Verification System (PVS) has been used for requirements analysis of one module of a physical access control system. PVS is a tool for writing formal specifications and constructing proofs. Previously, the same requirements have been analyzed by means of testing supported by the IFAD Toolbox for VDM-SL. The capabilities of the two formal methods are compared

Towards a Framework for Formalizing Requirements

This paper presents a pragmatic approach for formalizing requirements. It has three main contributions: First, it provides a survey of publications dealing with the the construction of formal software requirements specifications. Second, two models of the formalization process are developed. The first model is a generic one whereas the second one incorporates the model-oriented specification language VDM-SL. To highlight the assumptions that are made on the capabilities of potential users, the models provide different kinds of services to idealized roles. Third, one of the characteristics of a good software requirements specification is discussed: Modifiability. Using the models defined previously, the impact of changing part of the informal requirements on the formal specification is discussed

Using PVS for Requirements Analysis of an Access Control ... Industrial Application Stream

This paper presents a case study in which a theorem prover has been used for requirements analysis of an existing industrial application. Based on the insights gained in the first step of a larger project, formally specifying an entire Access Control supported, by the IFAD toolbox, a core concept - believed to be error-prone - is analyzed by identifying and proving safety- and liveness properties. Major inconsistencies and ambiguities have been found, as illustrated by precise figures and examples. Both the formal PVS specification and the requirements are given in detail. Finally, analysis as part of the overall (formal) development process is discussed. It is shown how tools like VDM and PVS can be integrated efficiently