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Title Some Results on the Representation Theory of the Symplectic Similitude Group of Order Four
Publication Date
Date Accessioned
University/Publisher University of Illinois – Chicago
Abstract We compute the asymptotic expansion of Whittaker functions of an element of the maximal torus for principal series representations. We consider irreducible, reducible, and singular representations.
Subjects/Keywords Whittaker; asymptotic expansion; principal series; singular
Contributors Takloo-Bighash, Ramin (advisor); Shipley, Brooke (committee member); Shalen, Peter (committee member); Radford, David (committee member); Varma, Sandeep (committee member)
Language en
Rights Copyright 2012 Kathleen D. Dexter
Country of Publication us
Record ID handle:10027/9591
Repository uic
Date Retrieved
Date Indexed 2019-12-17
Issued Date 2012-12-13 00:00:00

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…of Whittaker functions on a proper subgroup of the maximal torus of GSp(4) to compute the remaining L-functions. The method he created uses the fact that the Whittaker functions appearing in the zeta integrals can be explicitly computed…

…which, in turn, allows one to explicitly compute the zeta integral and demonstrate that it does, in fact, represent the desired L-function. In this work, we use the method developed by Takloo-Bighash to compute the asymptotic expansion of Whittaker

…to obtain a two variable zeta function involving both the degree four and the degree five Lfunctions of GSp(4). In Section 2.1, we begin with the description of the asymptotic expansion of a Whittaker function as a certain finite sum. Then…

…of Whittaker functions, intertwining operators, and local coefficients. x CHAPTER 1 INTRODUCTION 1.1 The Representation Theory of GSp(4) 1.1.1 GSp(4) and Its Parabolic Subgroups Let F be a nonarchimedean local field of…

…x7B;π(n)v − ψ(n)v : n ∈ N, v ∈ V }. 1.1.4 Generic Representations and Whittaker Models Let θ be a smooth generic complex character of N . Here generic means that the restriction of θ to each simple root subgroups of N is non…

…functions W(π, θ) = {Wv |v ∈ V } is called a Whittaker model of π. The group G acts on this space by right translation π(h)W (g) = W (gh), and the map v → Wv intertwines V and W(π, θ). A…

Whittaker functional is a smooth linear functional Λ : V → C satisfying Λ(π(n)v) = θ(n)Λ(v). A Whittaker functional gives a Whittaker model by setting Wv (g) = Λ(π(g)v), 8 and a…

Whittaker model gives a Whittaker functional by defining Λ(v) = Wv (e), where e denotes the identity element of G. (When we need to specify to which representation Λ belongs, we will write Λπ . Otherwise, the subscript will be…