Super-Schur polynomials for affine super Yangian \(\mathsf{Y}(\widehat{\mathfrak{gl}}_{1|1})\)

DOI10.1007/JHEP08(2023)049arXiv2307.03150MaRDI QIDQ6050348

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Publication date: 12 October 2023

Published in: (Search for Journal in Brave)

Abstract: We explicitly construct cut-and-join operators and their eigenfunctions -- the Super-Schur functions -- for the case of the affine super-Yangian

m a t h s f Y (w i d e h a t {m a t h f r a k g l}_{1 | 1})

. This is the simplest non-trivial (semi-Fock) representation, where eigenfunctions are labeled by the superanalogue of 2d Young diagrams, and depend on the supertime variables

(p_{k}, h e t a_{k})

. The action of other generators on diagrams is described by the analogue of the Pieri rule. As well we present generalizations of the hook formula for the measure on super-Young diagrams and of the Cauchy formula. Also a discussion of string theory origins for these relations is provided.

Full work available at URL: https://arxiv.org/abs/2307.03150

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