In this paper, we study Whittaker modules for graded Lie algebras. We define Whittaker modules for a class of graded Lie algebras and obtain a one to one correspondence between the set of isomorphic classes of Whittaker modules and the set of ideals of a polynomial ring, parallel to a result from the classical setting and the case of the Virasoro algebra. As a consequence of this, we obtain a c...

Let A be the adeles of the function eld Fq (T). If E(g; s) is the Eisenstein series associated with the spherical vector in the principal series representation of the double cover of GL2(A), then the Fourier coeecients (Whittaker functions) of E(g; s) have an Euler product and satisfy a `Riemann Hypothesis' condition. Namely, the zeros occur only on the line <(s) = 0. These Whittaker functions ...

We give a constructive proof of the existence of the essential Whittaker function of a generic representation of GL(n, F ), for F a non-archimedean local field, using mirabolic restriction techniques. 2010 Mathematics Subject Classification: 22E50

The theory of Whittaker functions is of crucial importance in the classical study of automorphic forms on adele groups. Motivated by the appearance of Whittaker functions for covers of reductive groups in the theory of multiple Dirichlet series, we provide a study of Whittaker functions on metaplectic covers of reductive groups over local fields. Thesis Supervisor: Benjamin Brubaker Title: Assi...

Earlier work by the author and coworkers (Adams & Whittaker, 1948; Adams, 1949; Whittaker, 1949; Mounter & Whittaker, 1950; Mounter, 1951) has shown that the so-called 'true' or 'specific' cholinesterases of erythrocytes, brain and cobra venom, previously believed to act only on acetylcholine and a few other esters, are in reality capable of hydrolysing a wide range of non-choline esters, 3:3-d...

Some properties of sinc-approximations of continuous functions on a segment are studied. For the first time, the sinc-approximations arose in the work of Pleynet. Later, in connection with developments in signals coding theory, E. Borel and E. T. Whittaker introduced the notions of a cardinal function and a truncated cardinal function, the restriction of which to [0, π] looks like this:

biological diversity and species richness have been declined throughout the world as a result of human activities. measuring species richness is important in rangeland conservation to evaluate the status and trends of native plant species, detecting non-native species invasion and monitoring rare species. however, heterogeneity in plant distribution makes inventories difficult. in this study tw...

In previous work we introduced and studied a function R(a+, a−, c; v, v̂) that is a generalization of the hypergeometric function 2F1 and the Askey–Wilson polynomials. When the coupling vector c ∈ C is specialized to (b, 0, 0, 0), b ∈ C, we obtain a function R(a+, a−, b; v, 2v̂) that generalizes the conical function specialization of 2F1 and the q-Gegenbauer polynomials. The function R is the joi...

In this paper, we construct families of irreducible representations for a class of quantum groups Uq(fm(K)). First, we give a natural construction of irreducible weight representations for Uq(fm(K)) using methods in spectral theory developed by Rosenberg. Second, we study the Whittaker model for the center of Uq(fm(K)). As a result, the structure of Whittaker representations is determined, and ...

We study a 3–parametric family of stochastic point processes on the one–dimensional lattice originated from a remarkable family of representations of the infinite symmetric group. We prove that the correlation functions of the processes are given by determinantal formulas with a certain kernel. The kernel can be expressed through the Gauss hypergeometric function; we call it the hypergeometric ...