Representation theoretic interpretation and interpolation properties of inhomogeneous spin q-Whittaker polynomials
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29_2024_Article_930.pdf
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Author(s)
Korotkikh, Sergei
Date Issued
April 2, 2024
Journal
Selecta Mathematica
Publisher
Springer Science and Business Media LLC
Citation
Selecta Mathematica. 2024 Apr 02;30(3):40
Version
Final published version
Abstract
We establish new properties of inhomogeneous spin q-Whittaker polynomials, which are symmetric polynomials generalizing
$$t=0$$
t
=
0
Macdonald polynomials. We show that these polynomials are defined in terms of a vertex model, whose weights come not from an R-matrix, as is often the case, but from other intertwining operators of
$$U'_q({\widehat{\mathfrak {sl}}}_2)$$
U
q
′
(
sl
^
2
)
-modules. Using this construction, we are able to prove a Cauchy-type identity for inhomogeneous spin q-Whittaker polynomials in full generality. Moreover, we are able to characterize spin q-Whittaker polynomials in terms of vanishing at certain points, and we find interpolation analogues of q-Whittaker and elementary symmetric polynomials.
Subjects
General Physics and Astronomy
General Mathematics
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00029-024-00930-w
