Nonsymmetric Macdonald Superpolynomials

There are representations of the type-A Hecke algebra on spaces polynomials in anti-commuting variables. Luque and author [Sém. Lothar. Combin. 66 (2012), Art. B66b, 68 pages, arXiv:1106.0875] constructed nonsymmetric Macdonald taking values arbitrary modules algebra. In this paper two ideas combined to define study aforementioned polynomials, other words, superpolynomials. The modules, their orthogonal bases properties first derived. terms standard Young tableau approach these correspond hook tableaux. details Dunkl-Luque theory particular application presented. is an inner product for which mutually orthogonal. squared norms determined. By using techniques Baker Forrester [Ann. Comb. 3 (1999), 159-170, arXiv:q-alg/9707001] symmetric built up from theory. Here ''symmetric'' means sense, not classical group sense. a concise formula norm minimal polynomial, some formulas anti-symmetric polynomials. For both there factorization when evaluated at special points.