Last edited by Fecage
Friday, July 24, 2020 | History

4 edition of Degenerate principal series for symplectic groups found in the catalog.

Degenerate principal series for symplectic groups

by Chris Jantzen

  • 232 Want to read
  • 15 Currently reading

Published by American Mathematical Society in Providence, R.I .
Written in English

    Subjects:
  • p-adic fields.,
  • Symplectic groups.,
  • Representations of groups.,
  • Hecke algebras.

  • Edition Notes

    StatementChris Jantzen.
    SeriesMemoirs of the American Mathematical Society,, no. 488
    Classifications
    LC ClassificationsQA3 .A57 no. 488, QA247 .A57 no. 488
    The Physical Object
    Paginationxiii, 111 p. :
    Number of Pages111
    ID Numbers
    Open LibraryOL1737286M
    ISBN 100821825496
    LC Control Number92042412

    Degenerate principal series of classical groups: the phenomenon of long complementary series, preprint Tensor product of degenerate principal series and local theta correspondence Jan BibTeX @MISC{Ngoc98ageometric, author = {Do Ngoc and Diep and Truong Chi Trung}, title = {A GEOMETRIC REALIZATION OF DEGENERATE PRINCIPAL SERIES REPRESENTATIONS OF SYMPLECTIC GROUPS}, year = {}}.

    quotient of the degenerate principal series representation of a metaplectic or a quasisplit even unitary group. The subquotient occurs as a local component of an automorphic representation generated by a certain holomorphic cusp form. 1. Introduction In his long-awaited book [1], Arthur established a classi cation of irreducible. In mathematics, the principal series representations of certain kinds of topological group G occur in the case where G is not a compact group. There, by analogy with spectral theory, one expects that the regular representation of G will decompose according to some kind of continuous spectrum.

    We apply techniques introduced by Clerc, Kobayashi, Orsted and Pevzner to study the degenerate principal series of Sp(n,C). An explicit description of the K-types is provided and Knapp-Stein normalised operators are realised a symplectic Fourier transforms, and their K-spectrum explicitely computed. Reducibility phenomena are analysed in terms of K-types and Author: Pierre Clare. We explicitly (in terms of Langlands parameters) describe the image of the degenerate Eisenstein series in the case of a symplectic group. We study these series for any maximal parabolic subgroup and any Grossencharacter. We do that by an explicit analysis of the constant term of the Eisenstein by: 2.


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Degenerate principal series for symplectic groups by Chris Jantzen Download PDF EPUB FB2

Degenerate Principal Series for Symplectic Groups Base Product Code Keyword List: memo; MEMO; Degenerate Principal Series for Symplectic Groups. Author(s) (Product display): Chris Jantzen.

Abstract: This paper is concerned with induced representations for \(p\)-adic groups. In particular, Jantzen examines the question of reducibility in. Degenerate principal series for symplectic groups About this Title. Chris Jantzen. Publication: Memoirs of the American Mathematical Society Publication Year VolumeNumber ISBNs: (print); (online)Cited by: Degenerate principal series for symplectic groups Add library to Favorites Please choose whether or not you want other users to be able to see on your profile that this library.

In particular, it Degenerate principal series for symplectic groups book concerned with representations obtained by inducing a one-dimensional representation from a maximal parabolic subgroup (i.e., degenerate principal series representations). Using the Jacquet module techniques of Tadić, the reducibility points for such representations are determined.

Indeed, analogous results were recently obtained in [14] for special ear groups, using techniques of [1]. Outline The article is organised as follows: general notations are fixed and elementary facts regard- g degenerate principal series of the complex symplectic groups are stated in Cited by: 8.

DEGENERATE REPRESENTATIONS OF THE SYMPLECTIC GROUPS I. THE COMPACT GROUP Sp(n) I. INTRODUCTION Many attempts have been made in the last few years to understand the properties of physical systems such as elementary particles, the hydrogen atom, nuclei etc., using the theory of representations of the underlying symmetry group.

The structure composition series of generalized and degenerate principal series for Sp(4,F), Fp–adic, was obtained earlier by Sally and Tadi´c in [24].

Their approach is based on Jacquet modules. This manuscript is an extension of the manuscript called ”The composi-tion series of generalized and degenerate principal series for Sp(2,R)”. by: Defined more abstractly as a classical group, the symplectic group is the set of linear transformations of a 2n-dimensional vector space over F which preserve a non-degenerate skew-symmetric bilinear form.

Such a vector space is called a symplectic vector space, and the symplectic group of an abstract symplectic vector space V is denoted Sp(V). The most degenerate irreducible representations of the symplectic group J.

Math. Phys. 21, (); / Bases for Irreducible Representations of the Unitary Group in the Symplectic Group Chain J. Math. Phys. 11, (); / Degenerate Representations of the Symplectic Groups II. The Noncompact Group Sp(p, q)Cited by: 4.

goes beyond degenerate principal series) • [12] for symplectic groups. • [2,13] for orthogonal groups. • [14] for type G2. • [8] for type F4.

The reason that such a study was not preformed for groups of type En before, is that Weyl groups of these types are extremely big and have complicated structure. For that reason,Author: Hezi Halawi, Avner Segal. Degenerate principal series for symplectic and odd orthogonal groups. [Chris Jantzen] Book, Internet Resource: All Authors / Contributors: Chris Jantzen.

Find more information about: ISBN: # Symplectic groups\/span> \u00A0\u00A0\u00A0 schema. We explicitly determine the image of the Eisenstein series and thus determine an automorphic realization of certain irreducible global representations of Sp 2n (A Q).

Mathematics Subject Classification. 11F70, 22E Key words and phrases. Automorphic representations, degenerate Eisenstein series, symplectic groups. A Heisenberg group can be defined for any symplectic vector space, and this is the typical way that Heisenberg groups arise.

A vector space can be thought of as a commutative Lie group (under addition), or equivalently as a commutative Lie algebra, meaning with trivial Lie Heisenberg group is a central extension of such a commutative Lie group/algebra: the symplectic.

ing degenerate principal series of the complex symplectic groups are stated in Section 2. In Section 3, we introduce certain Fourier transforms, establish some of their elementary proper-ties and use them to normalise Knapp–Stein operators in Proposition 1.

In Section 4, we study. Chris Jantzen has written: 'Degenerate principal series for symplectic and odd-orthogonal groups' -- subject(s): P-adic fields, Symplectic groups, Representations of groups.

On the degenerate principal series of complex symplectic groups Article in Journal of Functional Analysis (9) November with 18 Reads How we measure 'reads'Author: Pierre Clare.

Genre/Form: Electronic books: Additional Physical Format: Print version: Jantzen, Chris, Degenerate principal series for symplectic groups / Material Type.

Strictly speaking C(,t) should be called degenerate complementary series because there are complementary series associated with the principal series, which should be called complementary series ([Kos], [ABPTV]). Throughout this paper, complementary series will mean C(,t).

Let (Sp(p,R),Sp(n − p,R)) be a pair of symplectic groups diagonally embed. Get this from a library. Degenerate principal series for symplectic and odd-orthogonal groups. [Chris Jantzen] -- In this paper, we study p-adic fields, symplectic groups, orthogonal groups, and the reducibility of such representations.

We determine the reducibility points, give Langlands data and Jacquet. Degenerate principal series representations. Let us return back to the situation over real numbers, and we introduce degenerate principal series for G = Sp 2 n (R) and L = GL n (R) respectively. Degenerate principal series for G / P S.

Let us recall G = Sp 2 n (R) and its maximal parabolic subgroup P : Kyo Nishiyama, Bent Ørsted. Degenerate principal series for symplectic and odd-orthogonal groups / Material Type: Document, Internet resource: Document Type: Internet Resource, Computer File: All Authors / Contributors: Chris Jantzen.Degenerate principal series for symplectic groups - Chris Jantzen: MEMO/ Weak type estimates for Cesàro sums of Jacobi polynomial series - Sagun Chanillo and Benjamin Muckenhoupt: MEMO/ Enright-Shelton theory and Vogan’s problem for generalized principal series - Brian D.

Boe and David H. Collingwood: Volume Number Title; MEMO.The main purpose of this article is to supplement the authors' results on degenerate principal series representations of real symplectic groups with the analogous results for metaplectic : Shunsuke Yamana.