A hyperoctahedral analogue of the free lie algebra

  title={A hyperoctahedral analogue of the free lie algebra},
  author={Nantel Bergeron},
  journal={J. Comb. Theory, Ser. A},
  • N. Bergeron
  • Published 1 December 1991
  • Mathematics
  • J. Comb. Theory, Ser. A
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
Applications of the Brauer Complex: Card Shuffling, Permutation Statistics, and Dynamical Systems
By algebraic group theory, there is a map from the semisimple conjugacy classes of a finite group of Lie type to the conjugacy classes of the Weyl group. Picking a semisimple class uniformly at
On the free Lie algebra with multiple brackets
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The lattice of intersections of reflecting hyperplanes of a complex reflection group W may be considered as the poset of 1-eigenspaces of the elements of W. In this paper we replace 1 with an
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


Some Aspects of Groups Acting on Finite Posets
Free Differential Calculus, IV. The Quotient Groups of the Lower Central Series
The quotient groups Qn(G) =GnGn+i of the lower central series G = G1 D G, D G, D * * of a finitely generated group G are finitely generated abelian groups. Our object is to develop an algorithm for
Lyndon Words, Free Algebras and Shuffles
A Lyndon word is a primitive word which is minimum in its conjugation class, for the lexicographical ordering. These words have been introduced by Lyndon in order to find bases of the quotients of