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A minimal representation of the orthosymplectic Lie supergroup

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A minimal representation of the orthosymplectic Lie supergroup. / Barbier, Sigiswald; Frahm, Jan.
I: International Mathematics Research Notices, Bind 2021, Nr. 21, 11.2021, s. 16357-16420.

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

Harvard

Barbier, S & Frahm, J 2021, 'A minimal representation of the orthosymplectic Lie supergroup', International Mathematics Research Notices, bind 2021, nr. 21, s. 16357-16420. https://doi.org/10.1093/imrn/rnz228

APA

Barbier, S., & Frahm, J. (2021). A minimal representation of the orthosymplectic Lie supergroup. International Mathematics Research Notices, 2021(21), 16357-16420. https://doi.org/10.1093/imrn/rnz228

CBE

Barbier S, Frahm J. 2021. A minimal representation of the orthosymplectic Lie supergroup. International Mathematics Research Notices. 2021(21):16357-16420. https://doi.org/10.1093/imrn/rnz228

MLA

Barbier, Sigiswald og Jan Frahm. "A minimal representation of the orthosymplectic Lie supergroup". International Mathematics Research Notices. 2021, 2021(21). 16357-16420. https://doi.org/10.1093/imrn/rnz228

Vancouver

Barbier S, Frahm J. A minimal representation of the orthosymplectic Lie supergroup. International Mathematics Research Notices. 2021 nov.;2021(21):16357-16420. Epub 2019. doi: 10.1093/imrn/rnz228

Author

Barbier, Sigiswald ; Frahm, Jan. / A minimal representation of the orthosymplectic Lie supergroup. I: International Mathematics Research Notices. 2021 ; Bind 2021, Nr. 21. s. 16357-16420.

Bibtex

@article{a535a80134214478a0dd9e87f4cdd625,
title = "A minimal representation of the orthosymplectic Lie supergroup",
abstract = "We construct a minimal representation of the orthosymplectic Lie supergroup $OSp(p,q|2n)$, generalising the Schr\{"}odinger model of the minimal representation of $O(p,q)$ to the super case. The underlying Lie algebra representation is realized on functions on the minimal orbit inside the Jordan superalgebra associated with $\mathfrak{osp}(p,q|2n)$, so that our construction is in line with the orbit philosophy. Its annihilator is given by a Joseph-like ideal for $\mathfrak{osp}(p,q|2n)$, and therefore the representation is a natural generalization of a minimal representations to the context of Lie superalgebras. We also calculate its Gelfand--Kirillov dimension and construct a non-degenerate sesquilinear form for which the representation is skew-symmetric and which is the analogue of an $L^2$-inner product in the supercase. ",
keywords = "math.RT, 17B10, 17B60, 22E46, 58C50",
author = "Sigiswald Barbier and Jan Frahm",
note = "45 pages",
year = "2021",
month = nov,
doi = "10.1093/imrn/rnz228",
language = "English",
volume = "2021",
pages = "16357--16420",
journal = "International Mathematics Research Notices",
issn = "1073-7928",
publisher = "Oxford University Press",
number = "21",

}

RIS

TY - JOUR

T1 - A minimal representation of the orthosymplectic Lie supergroup

AU - Barbier, Sigiswald

AU - Frahm, Jan

N1 - 45 pages

PY - 2021/11

Y1 - 2021/11

N2 - We construct a minimal representation of the orthosymplectic Lie supergroup $OSp(p,q|2n)$, generalising the Schr\"odinger model of the minimal representation of $O(p,q)$ to the super case. The underlying Lie algebra representation is realized on functions on the minimal orbit inside the Jordan superalgebra associated with $\mathfrak{osp}(p,q|2n)$, so that our construction is in line with the orbit philosophy. Its annihilator is given by a Joseph-like ideal for $\mathfrak{osp}(p,q|2n)$, and therefore the representation is a natural generalization of a minimal representations to the context of Lie superalgebras. We also calculate its Gelfand--Kirillov dimension and construct a non-degenerate sesquilinear form for which the representation is skew-symmetric and which is the analogue of an $L^2$-inner product in the supercase.

AB - We construct a minimal representation of the orthosymplectic Lie supergroup $OSp(p,q|2n)$, generalising the Schr\"odinger model of the minimal representation of $O(p,q)$ to the super case. The underlying Lie algebra representation is realized on functions on the minimal orbit inside the Jordan superalgebra associated with $\mathfrak{osp}(p,q|2n)$, so that our construction is in line with the orbit philosophy. Its annihilator is given by a Joseph-like ideal for $\mathfrak{osp}(p,q|2n)$, and therefore the representation is a natural generalization of a minimal representations to the context of Lie superalgebras. We also calculate its Gelfand--Kirillov dimension and construct a non-degenerate sesquilinear form for which the representation is skew-symmetric and which is the analogue of an $L^2$-inner product in the supercase.

KW - math.RT

KW - 17B10, 17B60, 22E46, 58C50

U2 - 10.1093/imrn/rnz228

DO - 10.1093/imrn/rnz228

M3 - Journal article

VL - 2021

SP - 16357

EP - 16420

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 21

ER -