We propose a very general construction of simple Virasoro modules generalizing and including both highest weight and Whittaker modules. This reduces the problem of classification of simple Virasoro modules which are locally finite over a positive part to classification of simple modules over a family of finite dimensional solvable Lie algebras. For one of these algebras all simple modules are c...

We construct families of irreducible representations for a class of quantum groups Uq(fm(K,H). First, we realize these quantum groups as Hyperbolic algebras. Such a realization yields natural families of irreducible weight representations for Uq(fm(K,H)). Second, we study the relationship between Uq(fm(K,H)) and Uq(fm(K)). As a result, any finite dimensional weight representation of Uq(fm(K,H))...

Abstract: QQ-plots are extremely useful in univariate data analysis. In this article, Koltchinskii (1997) and Chaudhuri’s (1996) definition of multivariate quantile is used to develop analogous plots for bivariate data. Bivariate qq-plots are exhibited for comparing a sample to a given population distribution (the bivariate normal), and for comparing two or more bivariate samples. The plots are...

Multi-scale modeling of Arctic tundra vegetation requires characterization of the heterogeneous tundra landscape, which includes representation of distinct plant functional types (PFTs). We combined high-resolution multi-spectral remote sensing imagery from the WorldView-2 satellite with light detecting and ranging (LiDAR)-derived digital elevation models (DEM) to characterize the tundra landsc...

Let F be a p-adic field, and Gn one of the groups GL(n, F ), GSO(2n−1, F ), GSp(2n, F ), or GSO(2(n − 1), F ). Using the mirabolic subgroup or analogues of it, and related “derivative” functors, we give an asymptotic expansion of functions in the Whittaker model of generic representations of Gn, with respect to a minimal set of characters of subgroups of the maximal torus. Denoting by Zn the ce...

1 ________________________________________________________________________ Authors' addresses: 1) Steve Whittaker, Sheffield University, Sheffield, S1 2TN, UK; 2) Quentin Jones, New Jersey Institute of Technology, Newark, NJ, 07102, USA; 3) Bonnie Nardi, University of California, Irvine, CA 92697, USA; 4) Michael Creech, BlueOak Software, Los Altos, CA, 94024, USA; 5) Loren Terveen, University ...

The principal series representations of the n-fold metaplectic covers of the general linear group GLr(F) were described in the foundational paper “Metaplectic Forms,” by Kazhdan and Patterson (1984). In this paper, we study the local coefficient matrices for a certain class of principal series representations over GL2(F), where F is a nonarchimedean local field. The local coefficient matrices c...

Natural resource management decision making generally requires the analysis of a variety of environmental, social and economic information, incorporating value judgement and policy and management goals. Justifiable decisions depend on the logical and transparent combination and analysis of information. This chapter describes the application of spatial multi-criteria analysis to natural resource...

Here W is in the Whittaker model W(π, ψ) of a unitary generic representation π of GL(n, F) and W ′ in W(π ′, ψ) where π ′ is a unitary generic representation of GL(n − 1, F) (see below for unexplained notations). One of the difficulties of the theory is that the representations π and π ′ need not be tempered. Thus one is led to consider holomorphic fiber bundles of representations (πu) and (π ′...