Symmetry breaking for representations of rank one orthogonal groups / Toshiyuki Kobayashi, Birgit Speh.

Format:

Book

Author/Creator:

Kobayashi, Toshiyuki, 1962-

Contributor:

Speh, Birgit, 1949-

Series:

Memoirs of the American Mathematical Society ; 0065-9266 no. 1126.

Memoirs of the American Mathematical Society, 0065-9266 ; volume 238, number 1126

Language:

English

Subjects (All):

Broken symmetry (Physics).

Operator spaces.

Banach spaces.

Group theory.

Physical Description:

v, 112 pages : illustrations ; 26 cm

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2015]

Contents:

Ch. 1 Introduction

ch. 2 Symmetry breaking for the spherical principal series representations

2.1.Notation and review of previous results

2.2.Finite-dimensional subquotients of disconnected groups

2.3.Symmetry breaking operators and spherical principal series representations

2.4.Multiplicities for composition factors

ch. 3 Symmetry breaking operators

3.1.Restriction of representations and symmetry breaking operators

3.2.Distribution kernels of symmetry breaking operators

3.3.Differential intertwining operators

3.4.Smooth representations and intertwining operators

3.5.Symmetry breaking operators for principal series representations

3.6.Meromorphic continuation of symmetry breaking operators

ch. 4 More about principal series representations

4.1.Models of principal series representations

4.2.Explicit K-finite functions in the non-compact model

4.3.Normalized Knapp

Stein intertwining operator

ch. 5 Double coset decomposition P'\G/P

ch. 6 Differential equations satisfied by the distribution kernels of symmetry breaking operators

6.1.A system of differential equations for symmetry breaking operators

6.2.The solutions Sol(Rn

{0}; [MARC+6E], [MARC+70])

ch. 7 K-finite vectors and regular symmetry breaking operators A[MARC+6E],[MARC+70]

7.1.Distribution kernel KA[MARC+6E][MARC+70] and its normalization

7.2.Preliminary results

7.3.Proof of Proposition 7.3

ch. 8 Meromorphic continuation of regular symmetry breaking operators KA[MARC+6E][MARC+70]

8.1.Recurrence relations of the distribution kernels KA[MARC+6E][MARC+70]

8.2.Functional equations

8.3.8.3 Support of KA[MARC+6E][MARC+70]

8.4.Renormalization KA[MARC+6E][MARC+70] for [MARC+70] -N

ch. 9 Singular symmetry breaking operator B[MARC+6E][MARC+70]

9.1.Singular symmetry breaking operator B[MARC+6E][MARC+70]

9.2.K-finite vectors and singular operators B[MARC+6E][MARC+70]

9.3.Proof of Theorem 9.1

9.4.Support of the distribution kernel of B[MARC+6E][MARC+70]

9.5.Renormalization B[MARC+6E][MARC+70] for ([MARC+6E], [MARC+70]) Leven with n odd

ch. 10 Differential symmetry breaking operators

10.1.Power of the Laplacian

10.2.Juhl's family of differential operators

10.3.The kernel of the differential symmetry breaking operator C[MARC+6E][MARC+70]

ch. 11 Classification of symmetry breaking operators

11.1.Classification of symmetry breaking operators

11.2.Strategy of the proof of Theorem 11.1

11.3.Lower bounds of the multiplicities

11.4.Extension of solutions from Rn

{0} to Rn

11.5.Regular symmetry breaking operators

11.6.Singular symmetry breaking operators

ch. 12 Residue formulae and functional identities

12.1.Residues of symmetry breaking operators

12.2.Functional equations satisfied by singular symmetry breaking operators

ch. 13 Image of symmetry breaking operators

13.1.Finite-dimensional image for [MARC+70] -N

13.2.Image for [MARC+70] m + N

13.3.Spherical vectors and symmetry breaking operators

ch. 14 Application to analysis on anti-de Sitter space

14.1.Harmonic analysis on Lorentzian hyperbolic spaces

14.2.Application of symmetry breaking operators to anti-de Sitter spaces

14.3.Analysis on vector bundles over anti-de Sitter spaces

ch. 15 Application to branching laws of complementary series

15.1.Discrete spectrum in complementary series

15.2.L2-model of complementary series representations

ch. 16 Appendix

16.1.Gegenbauer polynomials

16.2.Af-Bessel function and its renormalization

16.3.Zuckerman derived functor modules Aq ([MARC+6E]).

Notes:

Includes bibliographical references (pages 109-110).

ISBN:

9781470419226

147041922X

OCLC:

916408495

Publisher Number:

9781470419226