منابع مشابه
On the Weyl Representation of Metaplectic Operators
Abstract. We study the Weyl representation of metaplectic operators associated to a symplectic matrix having no non-trivial fixed point, and justify a formula suggested in earlier work of Mehlig and Wilkinson. We give precise calculations of the associated Maslovtype indices; these indices intervene in a crucial way in Gutzwiller’s formula of semiclassical mechanics, and are simply related to a...
متن کاملMETAPLECTIC OPERATORS ON C n by HANS
The metaplectic representation describes a class of automorphisms of the Heisenberg group H = H(G), defined for a locally compact abelian groupG. ForG = R ,H is the usual Heisenberg group. For the case when G is the finite cyclic group Zn, only partial constructions are known. Here we present new results for this case and we obtain an explicit construction of the metaplectic operators on C. We ...
متن کاملOn the Mehlig-wilkinson Representation of Metaplectic Operators
We study the Weyl representation of metaplectic operators suggested by earlier work of Mehlig and Wilkinson. We give precise calculations for the associated Maslov indices; these intervene in a crucial way in the Gutzwiller formula of semiclassical mechanics.
متن کاملMetaplectic Operators for Finite Abelian Groups and R
The Segal–Shale–Weil representation associates to a symplectic transformation of the Heisenberg group an intertwining operator, called metaplectic operator. We develop an explicit construction of metaplectic operators for the Heisenberg group H(G) of a finite abelian group G, an important setting in finite time-frequency analysis. Our approach also yields a simple construction for the multivari...
متن کاملWhittaker Functions on Metaplectic Groups
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...
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ژورنال
عنوان ژورنال: The Quarterly Journal of Mathematics
سال: 2007
ISSN: 0033-5606,1464-3847
DOI: 10.1093/qmath/ham023