Quasisymmetric functions and Heisenberg doubles
Keywords:
Quasisymmetric function, Heisenberg double, Tower of algebras, Hopf algebra, Fock spaceAbstract
The ring of quasisymmetric functions is free over the ring of symmetric functions. This result was previously proved by M. Hazewinkel combinatorially through constructing a polynomial basis for quasisymmetric functions. The recent work by A. Savage and O. Yacobi on representation theory provides a new proof to this result. In this paper, we proved that under certain conditions, the positive part of a Heisenberg double is free over the positive part of the corresponding projective Heisenberg double. Examples satisfying the above conditions are discussed.
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