Geometry and the compression of combinatorial formulas for Macdonald polynomals

• Applicant: Professor Dr. Peter Littelmann
• Subject Area: Mathematics
• Term: from 2009 to 2013
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 125974108

The aim of the project is to give a better understanding of the connection between the work of Gaussent, Littelmann, Schwer, Ram and Yip and the work of Haglund, Haiman and Loehr [3,4,5]. Both methods lead to rather different combinatorial formulas for Macdonald polynomials. It is expected that the connection between these formulas has a geometric background. The project has a geometric and a combinatorial part. The aim of the geometric part is to generalize the methods developed in [2] by Gaussent and Littelmann to a different class of Bott-Samelson varieties. The combinatorial part has as a goal to translate "geometry = counting points in a certain variety over a finite field with q elements" into a statistic on (generalized) Young diagrams producing a polynomial in q describing exactly the desired number.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1388: Representation Theory