Barbasch-Sahi algebras and Dirac cohomology

Flake, Johannes

doi:10.48550/arxiv.1608.07509

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2017

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“…Ciubotaru and He [8] introduces extended Dirac cohomology which relates the tempered modules of the graded Hecke algebra with the irreducible representations of W . A general umbrella framework for all of these examples was described by Flake [9].…”

Section: Introductionmentioning

confidence: 99%

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

Calvert

2017

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In this paper we will 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. In [8] Ciubotaru and He, 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 derived the branching graph using Dirac theory and combinatorics relating to the cohomology of Borel varieties Be of g and were able to use Dirac cohomology to construct an explicit model for the projective representations. We also described Vogan's morphism for Hecke algebras in type A using spectrum data of the Jucys-Murphy elements.

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Section: Introductionmentioning

confidence: 99%

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

Calvert

2017

Preprint

View full text Add to dashboard Cite

show abstract

Barbasch-Sahi algebras and Dirac cohomology

Cited by 1 publication

References 0 publications

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

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

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