Wreath Macdonald polynomials as eigenstates

2019/04/10 by Wen, Joshua Jeishing · 2 citations
#05E05 #81R50 #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1904.05015

Abstract

We show that the wreath Macdonald polynomials for ℤ/ℓℤ\wrΣ_n, when naturally viewed as elements in the vertex representation of the quantum toroidal algebra U_\mathfrakq,\mathfrakd(\mathfraksl_ℓ), diagonalize its horizontal Heisenberg subalgebra. Our proof makes heavy use of shuffle algebra methods, and we also obtain a new proof of existence of wreath Macdonald polynomials.

Cited by

• Quantum Trigonometric Spin Ruijsenaars-Schneider Models from K-theoretic Coulomb Branches
• Ext operators for wreath Macdonald polynomials

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