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Shift operators, residue families and degenerate Laplacians

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Shift operators, residue families and degenerate Laplacians. / Juhl, Andreas; Orsted, Bent.
In: Pacific Journal of Mathematics, Vol. 308, No. 1, 12.2020, p. 103-160.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Vancouver

Juhl A, Orsted B. Shift operators, residue families and degenerate Laplacians. Pacific Journal of Mathematics. 2020 Dec;308(1):103-160. doi: 10.2140/pjm.2020.308.103

Author

Juhl, Andreas ; Orsted, Bent. / Shift operators, residue families and degenerate Laplacians. In: Pacific Journal of Mathematics. 2020 ; Vol. 308, No. 1. pp. 103-160.

Bibtex

@article{d3501f1859fd4c3cb18db21dba8c5aa1,

title = "Shift operators, residue families and degenerate Laplacians",

abstract = "In this paper, we introduce new aspects in conformal geometry of some very natural second-order differential operators. These operators are termed shift operators. In the flat space, they are intertwining operators which are closely related to symmetry breaking differential operators. In the curved case, they are closely connected with ideas of holography and the works of Fefferman-Graham, Gover-Waldron and one of the authors. In particular, we obtain an alternative description of the so-called residue families in conformal geometry in terms of compositions of shift operators. This relation allows easy new proofs of some of their basic properties. In addition, we derive new holographic formulas for Q-curvatures in even dimension. Since these turn out to be equivalent to earlier holographic formulas, the novelty here is their conceptually very natural proof. The overall discussion leads to a unification of constructions in representation theory and conformal geometry.",

keywords = "Poincare metrics, ambient metrics, conformal geometry, symmetry breaking operators, residue families, shift operators, GJMS operators, Q-curvature, CONFORMALLY INVARIANT POWERS, GJMS-OPERATORS, EINSTEIN, FORMULAS, METRICS",

author = "Andreas Juhl and Bent Orsted",

year = "2020",

month = dec,

doi = "10.2140/pjm.2020.308.103",

language = "English",

volume = "308",

pages = "103--160",

journal = "Pacific Journal of Mathematics",

issn = "0030-8730",

publisher = "Mathematical Sciences Publishers",

number = "1",

}

RIS

TY - JOUR

T1 - Shift operators, residue families and degenerate Laplacians

AU - Juhl, Andreas

AU - Orsted, Bent

PY - 2020/12

Y1 - 2020/12

N2 - In this paper, we introduce new aspects in conformal geometry of some very natural second-order differential operators. These operators are termed shift operators. In the flat space, they are intertwining operators which are closely related to symmetry breaking differential operators. In the curved case, they are closely connected with ideas of holography and the works of Fefferman-Graham, Gover-Waldron and one of the authors. In particular, we obtain an alternative description of the so-called residue families in conformal geometry in terms of compositions of shift operators. This relation allows easy new proofs of some of their basic properties. In addition, we derive new holographic formulas for Q-curvatures in even dimension. Since these turn out to be equivalent to earlier holographic formulas, the novelty here is their conceptually very natural proof. The overall discussion leads to a unification of constructions in representation theory and conformal geometry.

AB - In this paper, we introduce new aspects in conformal geometry of some very natural second-order differential operators. These operators are termed shift operators. In the flat space, they are intertwining operators which are closely related to symmetry breaking differential operators. In the curved case, they are closely connected with ideas of holography and the works of Fefferman-Graham, Gover-Waldron and one of the authors. In particular, we obtain an alternative description of the so-called residue families in conformal geometry in terms of compositions of shift operators. This relation allows easy new proofs of some of their basic properties. In addition, we derive new holographic formulas for Q-curvatures in even dimension. Since these turn out to be equivalent to earlier holographic formulas, the novelty here is their conceptually very natural proof. The overall discussion leads to a unification of constructions in representation theory and conformal geometry.

KW - Poincare metrics

KW - ambient metrics

KW - conformal geometry

KW - symmetry breaking operators

KW - residue families

KW - shift operators

KW - GJMS operators

KW - Q-curvature

KW - CONFORMALLY INVARIANT POWERS

KW - GJMS-OPERATORS

KW - EINSTEIN

KW - FORMULAS

KW - METRICS

U2 - 10.2140/pjm.2020.308.103

DO - 10.2140/pjm.2020.308.103

M3 - Journal article

VL - 308

SP - 103

EP - 160

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 1

ER -