In mathematics, the metaplectic group Mp2n is a double cover of the symplectic group Sp2n. It can be defined over either real or p-adic numbers. The construction...

example the metaplectic group Mp2n is a double cover of the symplectic group Sp2n means that there are always two elements in the metaplectic group representing...

complex group and Abelian linear group, and is the Greek analog of "complex". The metaplectic group is a double cover of the symplectic group over R;...

might not be real forms of any complex group. A very important example of such a real group is the metaplectic group, which appears in infinite-dimensional...

orthogonal groups, which (in even dimension) doubly cover the projective orthogonal group. the metaplectic groups, which double cover the symplectic groups. The...

therefore has two possible holomorphic square roots. The metaplectic group is defined as the group Mp ⁡ ( 2 , R ) = { ( g , G ) | G ( z ) 2 = m ( g , z )...

modular group PSL(2, Z). Also closely related is the 2-fold covering group, Mp(2, R), a metaplectic group (thinking of SL(2, R) as a symplectic group). Another...

structure Table of Lie groups Anyon Orientation entanglement Pin group Pin(n) – two-fold cover of orthogonal group, O(n) Metaplectic group Mp(2n) – two-fold...

symplectic form, and their action on the Hilbert space is given by the Metaplectic group. The basic properties of the transformations mentioned above, such...

differential geometry, a metaplectic structure is the symplectic analog of spin structure on orientable Riemannian manifolds. A metaplectic structure on a symplectic...

associated to the metaplectic structure via the metaplectic representation. The metaplectic representation of the metaplectic group — the two-fold covering...

skulls Symplectite, in reference to a mineral intergrowth texture Metaplectic group Symplectomorphism This disambiguation page lists articles associated...

(such as the metaplectic group) are real reductive groups. On the other hand, the universal cover of SL(2,R) is not a real reductive group, even though...

More specifically, for every member of the metaplectic group (which is a double cover of the symplectic group) there is a corresponding quadratic Fourier...

cover H of SL(2,R), known as the metaplectic group, is a Lie group that cannot be viewed as a linear algebraic group over R. More strongly, H has no faithful...

SL2(Z) (or of the metaplectic group if k is half-integral) and a character ρ of Γ. A modular form f for this character and this group Γ transforms under...

theory, was done jointly with Leopoldt. He extended the concept of metaplectic group, in a way significant for arithmetic applications. This opened a field...

the local Langlands correspondence and the representation theory of metaplectic groups. Senior Wrangler, University of Cambridge (1994) American Mathematical...

of F {\displaystyle F} . There exists a Weil representation of the metaplectic group M p ( W ) {\displaystyle Mp(W)} associated to ψ {\displaystyle \psi...

equidistribution of the θp. This work involved automorphic forms for the metaplectic group, and Vaughan's lemma in analytic number theory. In 2000 further refinements...

forms on adele groups. Princeton University Press. 1975. ISBN 0691081565. Weil's representation and the spectrum of the metaplectic group. Springer. 1976...

mathematical induction. min – minimum of a set. mod – modulo. Mp – metaplectic group. mtanh – modified hyperbolic tangent function. (Also written as mth...

covering space. In mathematical terms, the covering group of the symplectic group is the metaplectic group, and De Gosson summarizes the mathematical reasons...

portal Mathematics portal Commutation theorem for traces Metaplectic group Symplectic group Symplectic spinor bundle Shale, D. (1962). "Linear symmetries...

table of some common Lie groups and their associated Lie algebras. The following are noted: the topological properties of the group (dimension; connectedness;...

1007/s002220050082 with Bump, Friedberg Eisenstein series on the metaplectic group and non vanishing theorems for automorphic L-functions and their derivatives...

specialized in the study of the Leray–Maslov index and in the theory of the metaplectic group, and their applications to mathematical physics. In 1998 de Gosson...

is double covered by the metaplectic group Mp(2n). An important projective representation of Sp(2n) comes from the metaplectic representation of Mp(2n)...

representations of elements of a reductive dual pair. Heisenberg group Metaplectic group Howe, Roger E. (1979), "θ-series and invariant theory" (PDF), in...

representations (by Weyl's construction), while other representations (like the metaplectic representation) exist in infinite dimensions. Roe Goodman; Nolan Wallach...