The homology of the Brauer algebras
arXiv:2009.11590 · doi:10.1007/s00029-021-00697-4
Abstract
This paper investigates the homology of the Brauer algebras, interpreted as appropriate Tor-groups, and shows that it is closely related to the homology of the symmetric group. Our main results show that when the defining parameter of the Brauer algebra is invertible, then the homology of the Brauer algebra is isomorphic to the homology of the symmetric group, and that when the parameter is not invertible, this isomorphism still holds in a range of degrees that increases with n.
arXiv comment28 pages
References in corpus (7)
- Representation theory and homological stability
- Stabilization for mapping class groups of 3-manifolds
- Homological stability for moduli spaces of high dimensional manifolds. I
- Homological stability for configuration spaces of manifolds
- Homology stability for outer automorphism groups of free groups
- Homological stability for the mapping class groups of non-orientable surfaces
- Homological stability for unordered configuration spaces