Spin Hecke algebras of finite and affine types

Details Spin Hecke algebras of finite and affine types Spin Hecke algebras of finite and affine types

2006-11-30

arxiv.org/abs/math/0611950v1

Advances in Math. 212 (2007), 723--748.

Mathematics

Representation Theory

24 pages, to appear in Adv. in Math

Scientific paper

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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