# Automorphic forms on the metaplectic group by Gelbart S. By Gelbart S.

Similar symmetry and group books

Rotations, quaternions, and double groups

This distinct monograph treats finite element teams as subgroups of the complete rotation team, offering geometrical and topological tools which permit a special definition of the quaternion parameters for all operations. a huge function is an easy yet entire dialogue of projective representations and their software to the spinor representations, which yield nice merits in precision and accuracy over the extra classical double staff process.

The theory of groups

Possibly the 1st actually well-known e-book committed basically to finite teams used to be Burnside's ebook. From the time of its moment variation in 1911 until eventually the looks of Hall's e-book, there have been few books of comparable stature. Hall's booklet continues to be thought of to be a vintage resource for basic effects at the illustration concept for finite teams, the Burnside challenge, extensions and cohomology of teams, \$p\$-groups and lots more and plenty extra.

Additional resources for Automorphic forms on the metaplectic group

Example text

It follows that p(U ), X/G\p(U) ¯ neighbourhood U of x such that U are disjoint open sets separating p(x) and p(y). 2 If G is not compact, X/G need not be Hausdorﬀ. Highly pathological examples may be constructed using smooth R-actions. 1 Regard the 2-torus T2 as R2 /Z2 . Given α ∈ R , deﬁne the R-action Φt : T2 → T2 by Φt (θ, ψ) = (θ + t, ψ + αt), mod Z2 . If α is irrational, then every orbit of Φt is dense in T2 . In this case the orbit space T2 /R has only one nonempty open set: T2 /R. For this, observe that if q : T2 → T2 /R denotes the orbit map then U ⊂ T2 /R is open if and only if q −1 (U ) is an open and Φt -invariant subset of T2 .

Since exp |L is a local diﬀeomorphism at the origin, we may choose L so that exp maps L diﬀeomorphically onto an open neighbourhood D of e ∈ H. 6 Haar measure We conclude the chapter by recalling the simple proof of the existence of Haar measure for a compact Lie group. 1 Let G be a compact Lie group. There exists a unique Borel probability measure on G which is invariant under both left and right translations. Proof. We prove existence and leave uniqueness to the reader. Suppose that dim(G) = m.

These results hold for real or June 21, 2007 9:41 40 WSPC/Book Trim Size for 9in x 6in DynamicsSymmetry Dynamics and Symmetry complex representations. 2 Although we make little use of characters in this book, we emphasize that character theory is a fundamental tool for the analysis of group representations, especially over the complex ﬁeld. 1 The F-representation (V, G) is irreducible if the only G-invariant F-linear subspaces of V are {0} and V . If there exist nontrivial invariant subspaces, (V, G) is reducible.