Séminaire Lotharingien de Combinatoire, 91B.57 (2024), 12 pp.
Milo Bechtloff Weising
Murnaghan-Type Representations of the Elliptic Hall Algebra
Abstract.
We construct a new family of graded representations
W~λ indexed by Young diagrams λ for the
positive elliptic Hall algebra E+ which generalizes the
standard E+ action on symmetric functions. These
representations have homogeneous bases of eigenvectors for the action
of the Macdonald element P0,1 ∈ E+ generalizing
the symmetric Macdonald functions. We find an explicit combinatorial
rule for the action of the multiplication
operators er[X]•
generalizing the Pieri rule for symmetric Macdonald functions.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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