Strict quantization of coadjoint orbits

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Standard

Strict quantization of coadjoint orbits. / Schmitt, Philipp.

I: Journal of Noncommutative Geometry, Bind 15, Nr. 4, 2021, s. 1181-1249.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Schmitt, P 2021, 'Strict quantization of coadjoint orbits', Journal of Noncommutative Geometry, bind 15, nr. 4, s. 1181-1249. https://doi.org/10.4171/JNCG/429

APA

Schmitt, P. (2021). Strict quantization of coadjoint orbits. Journal of Noncommutative Geometry, 15(4), 1181-1249. https://doi.org/10.4171/JNCG/429

Vancouver

Schmitt P. Strict quantization of coadjoint orbits. Journal of Noncommutative Geometry. 2021;15(4):1181-1249. https://doi.org/10.4171/JNCG/429

Author

Schmitt, Philipp. / Strict quantization of coadjoint orbits. I: Journal of Noncommutative Geometry. 2021 ; Bind 15, Nr. 4. s. 1181-1249.

Bibtex

@article{0d6d46f032be4a84b418cf2877cf99c4,
title = "Strict quantization of coadjoint orbits",
abstract = "For every semisimple coadjoint orbit O^ of a complex connected semisimple Lie group G^, we obtain a family of G^-invariant products ∗^ℏ on the space of holomorphic functions on O^. For every semisimple coadjoint orbit O of a real connected semisimple Lie group G, we obtain a family of G-invariant products ∗ℏ on a space A(O) of certain analytic functions on O by restriction. A(O), endowed with one of the products ∗ℏ, is a G-Fr{\'e}chet algebra, and the formal expansion of the products around ℏ=0 determines a formal deformation quantization of O, which is of Wick type if G is compact. Our construction relies on an explicit computation of the canonical element of the Shapovalov pairing between generalized Verma modules and complex analytic results on the extension of holomorphic functions.",
keywords = "Formal deformation quantization, strict quantization, coadjoint orbits, Verma modules, Shapovalov pairing, Stein manifolds",
author = "Philipp Schmitt",
year = "2021",
doi = "10.4171/JNCG/429",
language = "English",
volume = "15",
pages = "1181--1249",
journal = "Journal of Noncommutative Geometry",
issn = "1661-6952",
publisher = "European Mathematical Society Publishing House",
number = "4",

}

RIS

TY - JOUR

T1 - Strict quantization of coadjoint orbits

AU - Schmitt, Philipp

PY - 2021

Y1 - 2021

N2 - For every semisimple coadjoint orbit O^ of a complex connected semisimple Lie group G^, we obtain a family of G^-invariant products ∗^ℏ on the space of holomorphic functions on O^. For every semisimple coadjoint orbit O of a real connected semisimple Lie group G, we obtain a family of G-invariant products ∗ℏ on a space A(O) of certain analytic functions on O by restriction. A(O), endowed with one of the products ∗ℏ, is a G-Fréchet algebra, and the formal expansion of the products around ℏ=0 determines a formal deformation quantization of O, which is of Wick type if G is compact. Our construction relies on an explicit computation of the canonical element of the Shapovalov pairing between generalized Verma modules and complex analytic results on the extension of holomorphic functions.

AB - For every semisimple coadjoint orbit O^ of a complex connected semisimple Lie group G^, we obtain a family of G^-invariant products ∗^ℏ on the space of holomorphic functions on O^. For every semisimple coadjoint orbit O of a real connected semisimple Lie group G, we obtain a family of G-invariant products ∗ℏ on a space A(O) of certain analytic functions on O by restriction. A(O), endowed with one of the products ∗ℏ, is a G-Fréchet algebra, and the formal expansion of the products around ℏ=0 determines a formal deformation quantization of O, which is of Wick type if G is compact. Our construction relies on an explicit computation of the canonical element of the Shapovalov pairing between generalized Verma modules and complex analytic results on the extension of holomorphic functions.

KW - Formal deformation quantization

KW - strict quantization

KW - coadjoint orbits

KW - Verma modules

KW - Shapovalov pairing

KW - Stein manifolds

U2 - 10.4171/JNCG/429

DO - 10.4171/JNCG/429

M3 - Journal article

VL - 15

SP - 1181

EP - 1249

JO - Journal of Noncommutative Geometry

JF - Journal of Noncommutative Geometry

SN - 1661-6952

IS - 4

ER -

ID: 290040903