Geodesic
Equating inv-quinv formulas for the \(q\)-Whittaker and modified Hall-Littlewood functions
Aritra Bhattacharya1
1Beijing International Center for Mathematical Research, Peking University, Beijing, 100871, China
The electronic journal of combinatorics, Tome 32 (2025) no. 4
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The two combinatorial formulas for modified Macdonald polynomials given by Haglund, Haiman, and Loehr (2005) and by Ayyer, Mandelshtam, and Martin (2023) give two combinatorial interpretations of $q$-Whittaker functions and modified Hall-Littlewood functions. The main result of this paper is a combinatorial proof of the equality between these two formulas, using weighted Dyck path symmetric functions (introduced by Carlsson and Mellit, 2018) as intermediate objects. In the final section, we remark on the Schur positivity of these weighted Dyck path symmetric functions.
DOI : 10.37236/13676
Classification : 05E05, 33D52
Mots-clés : Macdonald polynomials, Schur positivity, weighted Dyck path symmetric functions

Aritra Bhattacharya  1

1 Beijing International Center for Mathematical Research, Peking University, Beijing, 100871, China 
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Aritra Bhattacharya. Equating inv-quinv formulas for the \(q\)-Whittaker and modified Hall-Littlewood functions. The electronic journal of combinatorics, Tome 32 (2025) no. 4. doi: 10.37236/13676

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