Séminaire Lotharingien de Combinatoire, 91B.61 (2024), 12 pp.
Aritra Bhattacharya, T V Ratheesh and Sankaran Viswanath
Monomial Expansions for q-Whittaker and Modified Hall-Littlewood Polynomials
Abstract.
We consider the monomial expansion of the q-Whittaker polynomials
given by the fermionic formula and via the inv and quinv
statistics. We construct bijections between the parametrizing sets of
these three models which preserve the x- and q-weights, and which
are compatible with natural projection and branching maps. We apply
this to the limit construction of local Weyl modules and obtain a new
character formula for the basic representation of
sl^n. Finally, we indicate how our main results
generalize to the modified Hall-Littlewood case.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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