Recursion and Explicit Formulas for Particular N-Variable Knop–Sahi and Macdonald Polynomials
✍ Scribed by Jennifer Morse
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 161 KB
- Volume
- 88
- Category
- Article
- ISSN
- 0097-3165
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✦ Synopsis
Knop and Sahi simultaneously introduced a family of non-homogeneous, non-symmetric polynomials, G : (x; q, t). The top homogeneous components of these polynomials are the non-symmetric Macdonald polynomials, E : (x; q, t). An appropriate Hecke algebra symmetrization of E : yields the Macdonald polynomials, P * (x; q, t). A search for explicit formulas for the polynomials G : (x; q, t) led to the main results of this paper. In particular, we give a complete solution for the case G (k, a, ..., a) (x; q, t). A remarkable by-product of our proofs is the discovery that these polynomials satisfy a recursion on the number of variables.