We prove a localization theorem for affine W-algebras in the spirit of Beilinson–Bernstein and Kashiwara–Tanisaki. More precisely, any non-critical regular weight λ, we identify λ-monodromic Whittaker D-modules on enhanced flag variety with full subcategory Category O W-algebra. To essential image our functor, provide new realization using Iwahori–Whittaker modules corresponding Kac–Moody algeb...

In this paper we establish a connection between the associated variety of a representation and the existence of certain degenerate Whittaker functionals, for both smooth and K-finite vectors, for all quasi-split real reductive groups, thereby generalizing results of Kostant, Matumoto and others.

Irreducible complex representations of GL(2) and SL(2) over a finite field can be classified by methods useful for p-adic reductive groups and real Lie groups. (See Piatetski-Shapiro’s inspiring A.M.S. Memoir on this subject.) That is, we first see that most principal series representations are irreducible. We determine the irreducible constituents of the irregular principal series. We prove th...

Several new formulas are developed that enable the evaluation of a family of definite integrals containing the product of two Whittaker Wk ,m(x)-functions. The integration is performed with respect to the second index m, and the first index k is permitted to have any complex value, within certain restrictions required for convergence. The method utilizes complex contour integration along with v...

1.1 Whittaker and Bessel models are of importance in the theory of automorphic representations of GSp4. This paper is the first in a series of two, where we study some phenomena corresponding to these models in the geometric Langlands program. The theory of Whittaker functors for GLn is an essential technical tool in Gaitsgory’s proof of the Vanishing Conjecture appearing in the geometric Langl...

1.1 One of the important technical tools in D. Gaitsgory’s proof of the Vanishing Conjecture appearing in the geometric Langlands correspondence ([3]) is the theory of Whittaker functors for GLn. In this paper we define analogous functors for GSp4 and study their properties. Let us first review the situation at the level of automorphic forms on G = Sp4. Let X be a smooth projective absolutely i...

The form of the species richness–productivity relationship (SRPR) remains central to our understanding of species diversity controls. Mittelbach et al. (2001) built on Waide et al. (1999) to provide the first largescale, formal meta-analysis of the SRPR, based on 257 data sets from 171 publications. Their aim was to classify each relationship as negative, positive, U shaped, or hump shaped, in ...