Intertwining operators for covering groups of SL(2) over a local field
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Intertwining operators for covering groups of SL(2) over a local field

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Published .
Written in English

Book details:

LC ClassificationsMicrofilm 80067
The Physical Object
Paginationii, 27 l.
Number of Pages27
ID Numbers
Open LibraryOL1368295M
LC Control Number92895591

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covering (and modify the sl (m, R) if and only if it has type and imply that the only intertwining operators are multiples of the. identity mapping. We hav e. T 0: D : Pierre Mathonet. PDF | On Feb 1, , A. W. Knapp and others published Intertwining Operators for Semisimple Groups II | Find, read and cite all the research you need on ResearchGate.   We prove that this action ω k, a lifts to a unitary representation of the universal covering of SL (2,ℝ), and can even be extended to a holomorphic semigroup Ω k, a. In the k ≡0 case, our semigroup generalizes the Hermite semigroup studied by R. Howe (a =2) and the Laguerre semigroup studied by the second author with G. Mano (a =1).Cited by: Local L-Functions for Split Spinor Groups 1 c 2 c n 2 c n 1 c n pppp i c and of type D n if m = 2n with the following Dynkin diagram. 1 c 2 c n 3 c n 2 c c n 1 c n pppp ˆ ˆ ˆˆ Z Z ZZ This group is a double covering, as algebraic groups, of the group SO.

metic data. The classical example is the group Sl 2(Z) sitting in the real Lie group Sl 2(R) or the group Sl 2(Z[p 1]) as a subgroup of Sl 2(C), which has to be viewed as real Lie group (See..). Of course we may also consider Sl n(Z) ˆSl n(R) as an arithmetic group. We get a slightly more sophisticated example, if we start from a quadratic. and works well for the universal covering group. Essentially, we realize the under-lying Ind functor as a Howe type duality with respect to a degenerate principal series representation I(ǫ,v) of Spf(p + q,R) ([12]). Then we construct an induced intertwining operator for the induced representation under consideration from the. Computing natural intertwining operators among unramified principal series for SL(2,R). Meromorphic continuation in terms of the gamma function. Holomorphic discrete series (summed with antiholomorphic) detected. (Meromorphically continued) intertwining operators extend to smooth vectors. [Belyi's proof of a conjecture of Grothendieck (pdf)]. A nite group is a group with nite number of elements, which is called the order of the group. A group Gis a set of elements, g2G, which under some operation rules follows the common proprieties e: g 1 and g 2 2G, then g 1g 2 2G. ativity: g 1(g 2g 3) = (g 1g 2)g 3. e element: for every g2Gthere is an inverse g 1 2G, and g.

reps of the group SL(2,C), the universal covering group of SO(1,3,R). Section 4 deals in general with the notions of intertwiners and invari-ants, spherical harmonics and spherical functions. In sections 5, 6, 7 we review the irreps of SL(2,C) and obtain the spherical functions occurring in the state sum for relativistic spin networks. 2. The method of proof is to construct certain explicit zeta-integrals of Rankin-Selberg type which interpolate the relevant Langlands L-functions and can be analyzed via the theory of Eisenstein series and intertwining operators. This is the first time such an approach has been applied to such general classes of groups. Flensted-Jensen, M.: ‘A proof of the Plancherel formula for the universal covering group of SL(2,]R) using spectral theory and spherical functions’, in Séminaire de Théorie Spectrale, –73, Institut de Recherche Mathématique Avancée, Strasbourg, , Exposé 4. Google Scholar. Quantum Theory, Groups and Representations: An Introduction Revised and expanded version, under construction Peter Woit Department of Mathematics, Columbia University [email protected] Novem Intertwining operators and the metaplectic representation