The Hopf algebra of odd symmetric functions

Details The Hopf algebra of odd symmetric functions The Hopf algebra of odd symmetric functions

2011-07-28

arxiv.org/abs/1107.5610v1

Mathematics

Quantum Algebra

41 pages, 12 figures

Scientific paper

We consider a q-analogue of the standard bilinear form on the commutative ring of symmetric functions. The q=-1 case leads to a Z-graded Hopf superalgebra which we call the algebra of odd symmetric functions. In the odd setting we describe counterparts of the elementary and complete symmetric functions, power sums, Schur functions, and combinatorial interpretations of associated change of basis relations.

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