Spin Hecke algebras of finite and affine types
Representation Theory
2011-11-09 v1 Quantum Algebra
Abstract
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.
Keywords
Cite
@article{arxiv.math/0611950,
title = {Spin Hecke algebras of finite and affine types},
author = {Weiqiang Wang},
journal= {arXiv preprint arXiv:math/0611950},
year = {2011}
}
Comments
24 pages, to appear in Adv. in Math