Macdonald and Kerov polynomials
Theory and notation
- DEFINITIONS:
$$
\begin{array}{c}
{\rm Ker}^{(g)}_R\{ p\} = {\rm Schur}_{R}\{p\}
+ \sum_{{R'< R}} {\cal K}_{{R,R'}}^{(g)} \cdot {\rm Schur}_{R'}\{p\}
\\ \\
\widehat{{\rm Ker}}_R^{(g )}\{p\}
={\rm Schur}_{R}\{p\}\ + \ \sum_{ R'^\vee> R^\vee}
\widehat{\cal K}^{(g )}_{R'^\vee,R^\vee}\cdot{\rm Schur}_{R'}\{p\}
\end{array}
$$
$$
\Big< { p}^{\Delta}\Big| { p}^{\Delta'} \Big>^{(g)} =
\left(\prod_{i=1}^{l_\Delta} g_{\delta_i}\right)
\cdot z_\Delta \cdot \delta_{\Delta,\Delta'}
$$
$$
g_n^{\rm Mac} = \frac{\{q^n\}}{\{t^n\}}
$$
- MAPLE programs
- LISTS
- Macdonald polynomials and Kostka matrices:
levels 1-7,
8
- Kerov polynomials and Kostka-Kerov matrices:
levels 1-7,
8
- Dual Kerov polynomials and Kostka-Kerov matrices:
levels 1-7