The coefficient coalgebra of a symmetrized tensor space

Abstract

The coefficient coalgebra of r-fold tensor space and its dual, the Schur algebra, are generalized in such a way that the role of the symmetric group Σ _r is played by an arbitrary subgroup of Σ _r . The dimension of the coefficient coalgebra of a symmetrized tensor space is computed and the dual of this coalgebra is shown to be isomorphic to the analogue of the Schur algebra.

Keywords:

• coefficient coalgebra
• symmetrized tensor space
• Schur algebra

AMS Subject Classifications::

• 20G43
• 16T15

Acknowledgements

We thank the referee for some useful suggestions.