Spin Hecke algebras of finite and affine types

Weiqiang Wang

Spin Hecke algebras of finite and affine types

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arxiv math/0611950 v1 pith:F3C6FQMW submitted 2006-11-30 math.RT math.QA

Weiqiang Wang This is my paper · ORCID

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We introduce the spin Hecke algebra, which is a q-deformation of the spin symmetric group algebra, and its affine generalization. We establish an algebra isomorphism which relates our spin (affine) Hecke algebras to the (affine) Hecke-Clifford algebras of Olshanski and Jones-Nazarov. Relation between the spin (affine) Hecke algebra and a nonstandard presentation of the usual (affine) Hecke algebra is displayed, and the notion of covering (affine) Hecke algebra is introduced to provide a link between these algebras. Various algebraic structures for the spin (affine) Hecke algebra are established.

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Higher-level degenerate spin affine Hecke superalgebras
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Higher-level degenerate spin affine Hecke superalgebras are isomorphic (after Clifford tensor) to higher-level degenerate affine Hecke–Clifford superalgebras, hence Morita superequivalent.

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