The Classification of All Singular Nonsymmetric Macdonald Polynomials

The affine Hecke algebra of type A has two parameters q,t and acts on polynomials in N variables. There are important pairwise commuting sets elements the algebra: Cherednik operators Jucys–Murphy whose simultaneous eigenfunctions nonsymmetric Macdonald polynomials, basis vectors irreducible modules algebra, respectively. For certain parameter values, it is possible for special to be with equal corresponding eigenvalues both operators. These called singular polynomials. values form qm=t−n 2≤n≤N. a fixed parameter, span an module algebra. Colmenarejo author (SIGMA 16 (2020), 010) showed that there exist each these they coincide specializations isotype (a partition N) dn−1,n−1,…,n−1,r some d≥1. In present paper, shown no other