The norm and the evaluation of the Macdonald polynomials in superspace
Camilo Gonz\'alez, Luc Lapointe
TL;DR
This paper proves conjectured formulas for the norm and evaluation of Macdonald polynomials in superspace, extending known results to a supersymmetric setting using combinatorial data from Young diagrams.
Contribution
It provides the first rigorous proof of explicit formulas for Macdonald polynomials in superspace, generalizing classical Macdonald polynomial results.
Findings
Validated conjectured formulas for norm and evaluation in superspace
Formulas involve arm-lengths and leg-lengths of Young diagram cells
Specializes to classical Macdonald polynomial formulas
Abstract
We demonstrate the validity of previously conjectured explicit expressions for the norm and the evaluation of the Macdonald polynomials in superspace. These expressions, which involve the arm-lengths and leg-lengths of the cells in certain Young diagrams, specialize to the well known formulas for the norm and the evaluation of the usual Macdonald polynomials.
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