Evaluation of Nonsymmetric Macdonald Superpolynomials at Special Points

In a preceding paper the theory of nonsymmetric Macdonald polynomials taking values in modules Hecke algebra type A (Dunkl and Luque SLC 2012) was applied to such consisting anti-commuting variables, define superpolynomials. These depend on two parameters q,t are defined by means Yang–Baxter graph. The present determines subclass at special points 1,t,t2,… or 1,t−1,t−2,…. arguments use induction degree computations with products generators algebra. resulting formulas involve q,t-hook products. Evaluations also found for superpolynomials having restricted symmetry antisymmetry properties.