Abstract
AbstractWe 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.
Publisher
Springer Science and Business Media LLC
Reference47 articles.
1. Aggarwal, A., Borodin, A., Wheeler, M.: Colored Fermionic Vertex Models and Symmetric Functions (2021). arXiv:2101.01605
2. Aggarwal, A.: Dynamical stochastic higher spin vertex models. Sel. Math. 24, 2659–2735 (2018). arXiv:1704.02499
3. Brubaker, B., Bump, D., Friedberg, S.: Schur polynomials and the Yang–Baxter equation. Commun. Math. Phys. 308, 281–301 (2011). arXiv:0912.0911
4. Borodin, A., Korotkikh, S.: Inhomogeneous spin $$q$$-Whittaker polynomials (2021). arXiv:2104.01415
5. Bosnjak, S., Mangazeev, V.: Construction of $$R$$-matrices for symmetric tensor representations related to $$U_q(\widehat{sl_n})$$. J. Phys. A Math. Theor. 49 (2016). arXiv:1607.07968