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Dirac cohomology, the projective supermodules of the symmetric group and the Vogan morphism

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Dirac cohomology, the projective supermodules of the symmetric group and the Vogan morphism. / Calvert, Kieran.
In: The Quarterly Journal of Mathematics, Vol. 70, No. 2, 13.06.2019, p. 535-563.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Calvert, K 2019, 'Dirac cohomology, the projective supermodules of the symmetric group and the Vogan morphism', The Quarterly Journal of Mathematics, vol. 70, no. 2, pp. 535-563. https://doi.org/10.1093/qmath/hay057

APA

Calvert, K. (2019). Dirac cohomology, the projective supermodules of the symmetric group and the Vogan morphism. The Quarterly Journal of Mathematics, 70(2), 535-563. https://doi.org/10.1093/qmath/hay057

Vancouver

Calvert K. Dirac cohomology, the projective supermodules of the symmetric group and the Vogan morphism. The Quarterly Journal of Mathematics. 2019 Jun 13;70(2):535-563. Epub 2018 Nov 1. doi: 10.1093/qmath/hay057

Author

Calvert, Kieran. / Dirac cohomology, the projective supermodules of the symmetric group and the Vogan morphism. In: The Quarterly Journal of Mathematics. 2019 ; Vol. 70, No. 2. pp. 535-563.

Bibtex

@article{90be7dade0d54290ada3a38d7238a75e,
title = "Dirac cohomology, the projective supermodules of the symmetric group and the Vogan morphism",
abstract = "We derive an explicit description of the genuine projective representations of the symmetric group Sn using Dirac cohomology and the branching graph for the irreducible genuine projective representations of Sn. Ciubotaru and He [D. Ciubotaru and X. He, Green polynomials of Weyl groups, elliptic pairings, and the extended index. Adv. Math., 283:1–50, 2015], using the extended Dirac index, showed that the characters of the projective representations of Sn are related to the characters of elliptic-graded modules. We derive the branching graph using Dirac theory and combinatorics relating to the cohomology of Borel varieties ℬe of g and are able to use Dirac cohomology to construct an explicit model for the projective representations. We also describe Vogan{\textquoteright}s morphism for Hecke algebras in type A using spectrum data of the Jucys–Murphy elements.",
author = "Kieran Calvert",
year = "2019",
month = jun,
day = "13",
doi = "10.1093/qmath/hay057",
language = "English",
volume = "70",
pages = "535--563",
journal = "The Quarterly Journal of Mathematics",
issn = "0033-5606",
publisher = "Oxford University Press",
number = "2",

}

RIS

TY - JOUR

T1 - Dirac cohomology, the projective supermodules of the symmetric group and the Vogan morphism

AU - Calvert, Kieran

PY - 2019/6/13

Y1 - 2019/6/13

N2 - We derive an explicit description of the genuine projective representations of the symmetric group Sn using Dirac cohomology and the branching graph for the irreducible genuine projective representations of Sn. Ciubotaru and He [D. Ciubotaru and X. He, Green polynomials of Weyl groups, elliptic pairings, and the extended index. Adv. Math., 283:1–50, 2015], using the extended Dirac index, showed that the characters of the projective representations of Sn are related to the characters of elliptic-graded modules. We derive the branching graph using Dirac theory and combinatorics relating to the cohomology of Borel varieties ℬe of g and are able to use Dirac cohomology to construct an explicit model for the projective representations. We also describe Vogan’s morphism for Hecke algebras in type A using spectrum data of the Jucys–Murphy elements.

AB - We derive an explicit description of the genuine projective representations of the symmetric group Sn using Dirac cohomology and the branching graph for the irreducible genuine projective representations of Sn. Ciubotaru and He [D. Ciubotaru and X. He, Green polynomials of Weyl groups, elliptic pairings, and the extended index. Adv. Math., 283:1–50, 2015], using the extended Dirac index, showed that the characters of the projective representations of Sn are related to the characters of elliptic-graded modules. We derive the branching graph using Dirac theory and combinatorics relating to the cohomology of Borel varieties ℬe of g and are able to use Dirac cohomology to construct an explicit model for the projective representations. We also describe Vogan’s morphism for Hecke algebras in type A using spectrum data of the Jucys–Murphy elements.

U2 - 10.1093/qmath/hay057

DO - 10.1093/qmath/hay057

M3 - Journal article

VL - 70

SP - 535

EP - 563

JO - The Quarterly Journal of Mathematics

JF - The Quarterly Journal of Mathematics

SN - 0033-5606

IS - 2

ER -