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... group: Z/2. Z/2 enter kernel generators, one per line (ad for adjoint, 7 to abort): 1/2,0/2 enter inner class(es): u sorry, that inner class is not compatible with the weight lattice 3. Defining a real group We suppose the user has ...
... the real group . §8 . THE DISCRETE SERIES . We recall the definition and Harish - Chandra parametrization of the dis- crete series for reductive Lie groups . This can be viewed as a noncompact group version of Cartan's theory of the ...
... real groups . ( The definitions , statements and some of the proofs have nevertheless been constructed with more general fields in mind . ) Suppose G is a connected reductive complex algebraic group . A real form of G is an ...
... of real groups. We then point out how the twisting data (θ, ω) may be combined with individual representations and with L-packets. Spectral transfer pertains to only those tempered representations and L-packets which are preserved under ...
... the real group to its complexifi- cation . For a brief discussion of this and other references to the literature the reader may look up Helgason [ 1984 ] . Chapter 7. LP - Theory of Harish - Chandra Transform Notes on Chapter 6 299.
... group Mp(nk, R) (the two-sheeted cover of the real symplectic group Sp(nk, R)). The associated unitary representation will be the restriction to G6 of the oscillator representation of the metaplectic group. This representation already ...
... group G is fixed in advance and the question is asked: which free products A I >|<i€1Ai of non-trivial real groups embed as a hyperbolic subgroup in $9 (G) for this given group G? Our result is as follows.5 Theorem 10.5 Let G be a given ...
... the “real case” are proved in a manner quite analogous to the way they are proved in the “p-adic case”. Indeed, the material in this chapter is more strongly influenced by Harish-Chandra's work on p-adic groups than it is by that on real ...
... group of SO ( VC ) . Thus , it is a Lie group . Furthermore , if dim Ve ≥ 3 it is simply connected ( cf. 9.2 ) . 11.A.2.7 . We now look at groups associated with real forms of ( Vc , ( , ) ) . So fix a real form V. Let Spin ( V ) ...
... the real numbers with the sum is a commutative additive group, which just means that the additive notation is being used. 1.1.5 (Homomorphisms) A map f : G → G' between the groups G and G' is said to be a group homomorphism if f(xy) ...