Further Pieri-type formulas for the nonsymmetric Macdonald polynomials

Details Further Pieri-type formulas for the nonsymmetric Macdonald polynomials Further Pieri-type formulas for the nonsymmetric Macdonald polynomials

2010-08-04

arxiv.org/abs/1008.0892v1

Mathematics

Quantum Algebra

Scientific paper

The branching coefficients in the expansion of the elementary symmetric function multiplied by a symmetric Macdonald polynomial $P_\kappa(z)$ are known explicitly. These formulas generalise the known $r=1$ case of the Pieri-type formulas for the nonsymmetric Macdonald polynomials $E_\eta(z)$. In this paper we extend beyond the case $r=1$ for the nonsymmetric Macdonald polynomials, giving the full generalisation of the Pieri-type formulas for symmetric Macdonald polynomials. The decomposition also allows the evaluation of the generalised binomial coefficients $\tbinom{\eta }{\nu }_{q,t}$ associated with the nonsymmetric Macdonald polynomials.

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