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

**A minimal representation of the orthosymplectic Lie supergroup.** / Barbier, Sigiswald; Frahm, Jan.

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

Barbier, S & Frahm, J 2019, 'A minimal representation of the orthosymplectic Lie supergroup', *International Mathematics Research Notices*. https://doi.org/10.1093/imrn/rnz228

Barbier, S., & Frahm, J. (2019). A minimal representation of the orthosymplectic Lie supergroup. *International Mathematics Research Notices*. https://doi.org/10.1093/imrn/rnz228

Barbier S, Frahm J. 2019. A minimal representation of the orthosymplectic Lie supergroup. International Mathematics Research Notices. https://doi.org/10.1093/imrn/rnz228

Barbier, Sigiswald and Jan Frahm. "A minimal representation of the orthosymplectic Lie supergroup". *International Mathematics Research Notices*. 2019. https://doi.org/10.1093/imrn/rnz228

Barbier S, Frahm J. A minimal representation of the orthosymplectic Lie supergroup. International Mathematics Research Notices. 2019. https://doi.org/10.1093/imrn/rnz228

Barbier, Sigiswald ; Frahm, Jan. / **A minimal representation of the orthosymplectic Lie supergroup**. In: International Mathematics Research Notices. 2019.

@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 = "2019",

doi = "10.1093/imrn/rnz228",

language = "English",

journal = "International Mathematics Research Notices",

issn = "1073-7928",

publisher = "Oxford University Press",

}

TY - JOUR

T1 - A minimal representation of the orthosymplectic Lie supergroup

AU - Barbier, Sigiswald

AU - Frahm, Jan

N1 - 45 pages

PY - 2019

Y1 - 2019

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

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

ER -