133 citations · 1.4k across the 77 of their papers we have counts for
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The Hopf algebras of symmetric functions and quasisymmetric functions in non-commutative variables are free and cofree
Nantel Bergeron, Mike Zabrocki
We uncover the structure of the space of symmetric functions in non-commutative variables by showing that the underlined Hopf algebra is both free and co-free. We also introduce th…
Representations of Two-parameter Quantum Orthogonal and Symplectic Groups
Nantel Bergeron, Yun Gao, Naihong Hu
We investigate the finite-dimensional representation theory of two-parameter quantum orthogonal and symplectic groups that we found in [BGH] under the assumption that is…
Posets related to the connectivity set of Coxeter groups
Nantel Bergeron, Christophe Hohlweg, Mike Zabrocki
We define the notion of connectivity set for elements of any finitely generated Coxeter group. Then we define an order related to this new statistic and show that the poset is grad…
Grothendieck bialgebras, Partition lattices and symmetric functions in noncommutative variables
Nantel Bergeron, Christophe Hohlweg, Mercedes Rosas +1
We show that the Grothendieck bialgebra of the semi-tower of partition lattice algebras is isomorphic to the graded dual of the bialgebra of symmetric functions in noncommutative v…
Drinfel'd Doubles and Lusztig's Symmetries of Two-Parameter Quantum Groups
Nantel Bergeron, Yun Gao, Naihong Hu
We find the defining structures of two-parameter quantum groups corresponding to the orthogonal and the symplectic Lie algebras, which are realized as Drinfel'd…
Coloured peak algebras and Hopf algebras
Nantel Bergeron, Christophe Hohlweg
For a finite abelian group, we study the properties of general equivalence relations on $G_n=G^n\rtimes \SG_n$, the wreath product of with the symmetric group $\SG_n$, also…
Invariants and Coinvariants of the Symmetric Group in Noncommuting Variables
Nantel Bergeron, Christophe Reutenauer, Mercedes Rosas +1
We introduce a natural Hopf algebra structure on the space of noncommutative symmetric functions which was recently studied as a vector space by Rosas and Sagan. The bases for this…