On the intertwining differential operators from a line bundle to a vector bundle over the real projective space

Toshihisa Kubo; Bent Ørsted

doi:10.1016/j.indag.2024.05.008

On the intertwining differential operators from a line bundle to a vector bundle over the real projective space

Toshihisa Kubo^*
, Bent Ørsted

^*Corresponding author af dette arbejde

Institut for Matematik

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

Abstract

We classify and construct SL(n,R)-intertwining differential operators D from a line bundle to a vector bundle over the real projective space RPⁿ⁻¹ by the F-method. This generalizes a classical result of Bol for SL(2,R). Further, we classify the K-type formulas for the kernel Ker(D) and image Im(D) of D. The standardness of the homomorphisms φ corresponding to the differential operators D between generalized Verma modules is also discussed.

Originalsprog	Engelsk
Tidsskrift	Indagationes Mathematicae
Vol/bind	36
Nummer	1
Sider (fra-til)	270-301
Antal sider	32
ISSN	0019-3577
DOI	https://doi.org/10.1016/j.indag.2024.05.008
Status	Udgivet - jan. 2025

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10.1016/j.indag.2024.05.008

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abstract = "We classify and construct SL(n,R)-intertwining differential operators D from a line bundle to a vector bundle over the real projective space RPn−1 by the F-method. This generalizes a classical result of Bol for SL(2,R). Further, we classify the K-type formulas for the kernel Ker(D) and image Im(D) of D. The standardness of the homomorphisms φ corresponding to the differential operators D between generalized Verma modules is also discussed.",

keywords = "Bol operator, F-method, Generalized Verma module, Intertwining differential operator, K-type formula, Standard map",

author = "Toshihisa Kubo and Bent {\O}rsted",

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AU - Kubo, Toshihisa

AU - Ørsted, Bent

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N2 - We classify and construct SL(n,R)-intertwining differential operators D from a line bundle to a vector bundle over the real projective space RPn−1 by the F-method. This generalizes a classical result of Bol for SL(2,R). Further, we classify the K-type formulas for the kernel Ker(D) and image Im(D) of D. The standardness of the homomorphisms φ corresponding to the differential operators D between generalized Verma modules is also discussed.

AB - We classify and construct SL(n,R)-intertwining differential operators D from a line bundle to a vector bundle over the real projective space RPn−1 by the F-method. This generalizes a classical result of Bol for SL(2,R). Further, we classify the K-type formulas for the kernel Ker(D) and image Im(D) of D. The standardness of the homomorphisms φ corresponding to the differential operators D between generalized Verma modules is also discussed.

KW - Bol operator

KW - F-method

KW - Generalized Verma module

KW - Intertwining differential operator

KW - K-type formula

KW - Standard map

U2 - 10.1016/j.indag.2024.05.008

DO - 10.1016/j.indag.2024.05.008

M3 - Journal article

AN - SCOPUS:85195609562

SN - 0019-3577

VL - 36

SP - 270

EP - 301

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

IS - 1

ER -

On the intertwining differential operators from a line bundle to a vector bundle over the real projective space

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