Quantum symmetric functions

Details Quantum symmetric functions Quantum symmetric functions

2003-12-29

arxiv.org/abs/math/0312494v3

Communications in Algebra, Volume 33, Number 6 (2005), 1947-1978

Mathematics

Quantum Algebra

Final version. To appear in Communications in Algebra

Scientific paper

We study quantum deformations of Poisson orbivarieties. Given a Poisson manifold $(\mathbb{R}^{m},\alpha)$ we consider the Poisson orbivariety $(\mathbb{R}^{m})^{n}/S_{n}$. The Kontsevich star product on functions on $(\mathbb{R}^{m})^{n}$ induces a star product on functions on $(\mathbb{R}^{m})^{n}/S_{n}$. We provide explicit formulae for the case ${{\mathfrak h} \times {\mathfrak h}}/\mathcal{W}$, where ${\mathfrak h}$ is the Cartan subalgebra of a classical Lie algebra ${\mathfrak g}$ and $\mathcal{W}$ is the Weyl group of ${\mathfrak h}$. We approach our problem from a fairly general point of view, introducing Polya functors for categories over non-symmetric Hopf operads.

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