We develop efficient data-sparse representations to a class of high order tensors via a block many-fold Kronecker product decomposition. Such a decomposition is based on low separation-rank approximations of the corresponding multivariate generating function. We combine the Sinc interpolation and a quadrature-based approximation with hierarchically organised block tensor-product formats. Differ...

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...

We define a regularized theta lift for orthogonal groups over totally real fields generalizing work of Borcherds. The lift takes harmonic ‘Whittaker forms’ to automorphic Green functions and weakly holomorphic Whittaker forms to meromorphic modular forms on orthogonal groups with zeros and poles supported on special divisors.