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

Calvert, Kieran (2019) Dirac cohomology, the projective supermodules of the symmetric group and the Vogan morphism. The Quarterly Journal of Mathematics, 70 (2). pp. 535-563. ISSN 0033-5606

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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’s morphism for Hecke algebras in type A using spectrum data of the Jucys–Murphy elements.

Item Type:
Journal Article
Journal or Publication Title:
The Quarterly Journal of Mathematics
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2600
Subjects:
?? general mathematicsmathematics(all) ??
ID Code:
207077
Deposited By:
Deposited On:
16 Oct 2023 13:05
Refereed?:
Yes
Published?:
Published
Last Modified:
16 Jul 2024 12:09