2 edition of **Invariant tempered distributions on the reductive p-adic group GLn (IFp)** found in the catalog.

Invariant tempered distributions on the reductive p-adic group GLn (IFp)

Peter A. Mischenko

- 228 Want to read
- 2 Currently reading

Published
**1982**
by [s.n.] in Toronto
.

Written in English

**Edition Notes**

Thesis (Ph.D.)--University of Toronto, 1983.

Statement | Peter A. Mischenko. |

ID Numbers | |
---|---|

Open Library | OL14841303M |

INTRODUCTION TO THE THEORY OF ADMISSIBLE REPRESENTATIONS OF p-ADIC REDUCTIVE GROUPS W. CASSELMAN Draft: 1 May Preface This draft of Casselman’s notes was worked over by the S´eminaire Paul Sally in – In addition to File Size: KB. Get this from a library! Admissible invariant distributions on reductive p-adic groups. [Harish-Chandra.; Stephen DeBacker; Paul J Sally, Jr.] -- "Harish-Chandra presented these lectures on admissible invariant distributions for p-adic groups at the Institute for Advanced Study in the early s. He published a short sketch of this material.

p-adic groups end up to the problems on semi-invariant distributions of this kind. There are quite a lot of techniques on the vanishing of invariant distributions. It seems to us that the constructions of semi-invariant distributions are still not fully developed. We suggest in this paper that, to describe all semi-invariant distributions on the. COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.

An alternative proof of Theorem 1, based on an idea of D. Kazhdan, is being developed by V. Nistor and P. Schneider. A proof of the Baum-Connes conjecture for p-adic GL() 2. Periodic cyclic homology Let K be a compact open subgroup of G and let X(G, K) be the convolution algebra of compactly supported, K-bi-invariant functions on by: Schneider and Stuhler have defined Euler–Poincaré functions of irreducible representations of reductive p-adic groups and calculated their orbital l integrals belong to a larger family of invariant distributions appearing in the geometric side of the Arthur–Selberg trace : Hi-joon Chae, Ja Kyung Koo.

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p. -adic Groups. Harish-Chandra presented these lectures on admissible invariant distributions for p -adic groups at the Institute for Advanced Study in the early s.

He published a short sketch of this material as his famous “Queen's Notes”. Book Condition: Title: Admissible Invariant Distributions on Reductive p-adic Groups.

Ex University of California, Berkeley Astronomy/Mathematics/Statistics Library book with usual library markings. Binding is tight, text clean. No other marks in very lightly read book.

Softcover overbound with clear plastic by: tion product in D(G;K) that any invariant distribution, i.e. any element of D(G;K)G, is supported on a union of relatively compact conjugacy classes in G. If G is the group of L-rational points of a connected, reductive, linear algebraic group Gall of whose simple factors are L-isotropic (e.g.

an L-split. Let G be a p-adic connected reductive group with Lie algebra g. For a parabolic subgroup P in G and a finite-dimensional locally analytic representation V of P, we study the induced locally Author: Jan Kohlhaase. Admissible Invariant Distributions on Reductive P-adic Groups - Harish-Chandra - Google Books.

Harish-Chandra presented these lectures on admissible invariant distributions for p-adic groups at the Institute for Advanced Study in the early s. He published a short sketch of this material as his famous "Queen's Notes". We describe the unitary and tempered dual of the n-fold metaplectic covers of SL(2, F), where F is a p-adic field with p not dividing 2n.

Let p be a prime number, let L be a finite extension of the field Q p of p-adic numbers, let K be a spherically complete extension field of L, and let G be the group of L-rational points of a split reductive group over L. We derive several explicit descriptions of the center of the algebra D (G, K) of locally analytic distributions on G with Cited by: Abstract.

At the Williastown conference on harmonic analysis, R. Howe publicized two conjectures concerning the orbital integrals of functions on a reductive p-adic group and on its Lie proved the Lie algebra case of the conjecture himself; recently we have proved the conjecture on the group, at least in zero characteristic [4c,4d].Cited by: We also prove that Plancherel measure (on the tempered dual of a reductive p-adic group) is rotation-invariant.

(C) Ekevier Science (USA). Do you want to read the rest of this article?Author: Roger Plymen. Tempered Distributions The theory of tempered distributions allows us to give a rigorous meaning to the Dirac delta function. It is “deﬁned”, on a hand waving level, by the properties that (i) δ(x) = 0 except when x= 0 (ii) δ(0) is “so inﬁnite” that (iii) the area under its graph is Size: KB.

Let k be a p-adic field of characteristic zero, and let G be a connected reductive group defined over k. Let G be the group of k-rational points of G, and let g be the Lie algebra of : Stephen Debacker.

REPRESENTATIONS OF REDUCTIVE p-ADIC GROUPS Assume that G is (the rational points of) a reductive group over a p-adic eld: such a group is a locally compact topological group. There exists a measure on Gwhich is G-invariant: (gS) = (Sg) = (S), for g 2G, and S any invariant distribution on G: File Size: KB.

Abstract. Let H (G) be the Hecke algebra of a reductive p-adic group formulate a conjecture for the ideals in the Bernstein decomposition of H (G).The conjecture says that each ideal is geometrically equivalent to an algebraic variety.

Our conjecture is closely related to Lusztig’s conjecture on the asymptotic Hecke by: The goal of Murnaghan-Kirillov theory is to associate to an irreducible smooth rep-resentation of a reductive p-adic group a family of regular semisimple orbital integrals in the Lie algebra with.

Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. The purpose of this article is to discuss some questions in the harmonic analysis of real and p-adic groups.

We shall be particularly concerned with the properties of a certain family of invariant distributions. These distributions arose naturally in a global context, as the terms on the geometric side of the trace by: 3.

GENERALIZED SPHERICAL FUNCTIONS ON p-ADIC GROUPS also true for p-adic are many not so surprising similarities between our proofs for the p-adic case and that for the real case in [HOW] (but there are a number of diﬀerences). The Hecke algebra H(G) of compactly supported smooth functions on a p-adic group often plays a role similar to that of the universal en.

This chapter reviews the characters of reductive p-adic motivation for the results discussed by the author comes from the Lefschetz principle, which says that whatever is true for real groups should also be true for p-adic G be a compact, connected, real semisimple Lie group and g, its Li a Cartan subalgebra h and define Fourier transforms on g and by: An irreducible Markov chain has at most one invariant distribution.

It certainly has one if it is finite. The Markov chain is said to be positive recurrent if it has one invariant distribution. We noted earlier that the leftmost Markov chain of Figure has a unique invariant distribution that is given by ().

A locally pro nite group is a group Gsatisfying any one of the following equivalent conditions: G= lim Kopen compact G=K. Gis totally disconnected and locally compact. Example The basic examples are: Q p= S p kZ p.

Q p = pZ Z p. This illustrates two directions in which p-adic reductive groups di er from each other: Q pis unipotent, and Q p File Size: KB.

Tempered distributions and the Fourier transform Microlocal analysis is a geometric theory of distributions, or a theory of geomet-ric distributions. Rather than study general distributions { which are like general continuous functions but worse { we consider more speci c types of distributionsFile Size: KB.Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share .This chapter discusses the discrete series characters for reductive p-adic discrete series, which is well understood for real groups, has presented one of the most vexing problems in the representation theory of p-adic has been some progress in the construction of discrete series ([Hi], [KL], [Kub]), but only a few results exist on the specific nature of their by: