Representation Theory and Analysis on Homogeneous Spaces: A by Simon Gindikin, Roe Goodman, Frederick P. Greenleaf

By Simon Gindikin, Roe Goodman, Frederick P. Greenleaf

Combining presentation of latest effects with in-depth surveys of modern paintings, this booklet specializes in illustration conception and harmonic research on genuine and $p$-adic teams. The papers are in line with lectures provided at a convention devoted to the reminiscence of Larry Corwin and held at Rutgers collage in February 1993. The ebook offers a survey of harmonic research on nilpotent homogeneous areas, effects on multiplicity formulation for triggered representations, new tools for developing unitary representations of genuine reductive teams, and a unified therapy of hint Paley-Wiener theorems for actual and $p$-adic reductive groups.In the illustration concept of the final linear staff over $p$-adic fields, the ebook offers an outline of Corwin's contributions, a survey of the position of Hecke algebras, and a presentation of the idea of straightforward forms. different different types of reductive $p$-adic teams also are mentioned. one of the different themes integrated are the illustration conception of discrete rational nilpotent teams, skew-fields linked to quadratic algebras, and finite versions for percolation. A well timed e-book that includes contributions through many of the best researchers within the box, this booklet deals a point of view hardly ever present in convention court cases

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Extra info for Representation Theory and Analysis on Homogeneous Spaces: A Conference in Memory of Larry Corwin February 5-7, 1993 Rutgers University

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9) This means that the function F2 (i*) has a singularity for A = 0 or i* = 2 A* = = - (h -1 - 1) n, corresponding to an extreme case M --'> 00. This transformation may be very convenient in some cases and a more thorough discussion of it may be found in 1. Let us mention that because the quantity A = 1/2 (h -1 - 1) n represents an upper bound for A, it is obvious that for the upper bound of the variable T, the quantity io = (h- 1 - 1) n may be chosen. That quantity ro should be used in the considerations presented in section III.

2) converges very slowly, and it is therefore necessary to employ a large number of terms in order to obtain a good approximation for T*. 7), the number m must be chosen rather large. If this is the case, it is then expedient to replace the expansion (1. 2) by (1. 9). Theoretically, this is, however, not the only way of overcoming this difficulty, and in the following other means of doing so will be indicated: this alternative approach employs the method of analytic continuation. Let T (q, e) be determined in a domain, say H, and let Tn> n = 1,2, ...

Thus for A = 0, the quantity B = 0 and the function Fl -- 00. In some cases, however, it is possible to overcome this difficulty by shifting the origin. 1) '/ - '/ 2' so that A* will mean A* = A - ;, 7:* = 7: - a. 2) W 3*'1* + F2 (3*, 'YJ*) W = 0, 1 1 where W (3*, 'YJ*) = p* (3* + '2 a, 'YJ* + '2 a), F2 (7:*) = Fl (7:* + a), so that F2 is analytic for 7:* = O. * .. * E(n+l) (7:*) .. 3a) 1) (7:). 39 10. Transformation to the Physical Plane The domain of convergence, remaining the same, referred to the r* system, is merely a shift of the original domain.

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