Hyperoctahedral Operations on Hochschild Homology

@article{Bergeron1995HyperoctahedralOO,
  title={Hyperoctahedral Operations on Hochschild Homology},
  author={Nantel Bergeron},
  journal={Advances in Mathematics},
  year={1995},
  volume={110},
  pages={255-276}
}
  • N. Bergeron
  • Published 1 February 1995
  • Mathematics
  • Advances in Mathematics
Abstract We construct Families {ρ l, k n } of orthogonal idempotents of the hyperoctahedral group algebras Q [ B n ], which commute with the Hochschild boundary operators b n =∑ n i=0 (−1) i d i . We show that those idempotents are projections onto some hyperoactahedral symmetric powers of the free Lie algebra Lie ( l, k ) n ( A ). The commutations above then decompose the Hochshild homology H n ( C ) obtained by any functor C : Δ op → K - module that factor through Fin ′ B , the… 
Cohomology of Coxeter arrangements and Solomon's descent algebra
We refine a conjecture by Lehrer and Solomon on the structure of the Orlik-Solomon algebra of a finite Coxeter group $W$ and relate it to the descent algebra of $W$. As a result, we claim that both
Eulerian representations for real reflection groups
  • Sarah Brauner
  • Mathematics
    Journal of the London Mathematical Society
  • 2022
The Eulerian idempotents, first introduced for the symmetric group and later extended to all reflection groups, generate a family of representations called the Eulerian representations that decompose
Carries, shuffling, and symmetric functions
MATHEMATICAL DEVELOPMENTS FROM THE ANALYSIS OP RIFFLE SHUFFLING
1. Introduction The most common method of mixing cards is the ordinary riffle shuffle, in which a deck of n cards (often n = 52) is cut into two parts and the parts are riffled together. A sharp