English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We introduce difference operators on the space of symmetric functions whichare a natural generalization of the $(q,t)$-Macdonald operators. In the$t\to\infty$ limit, they satisfy the $A_{N-1}$ quantum $Q$-system. We identifythe elements in the spherical $A_{N-1}$ DAHA which are represented by theseoperators, as well as within the quantum toroidal algebra of $gl_1$ and theelliptic Hall algebra. We present a plethystic, or bosonic, formulation of thegenerating functions for the generalized Macdonald operators, which we relateto recent work of Bergeron et al. Finally we derive constant term identitiesfor the current that allow to interpret them in terms of shuffle products. Inparticular we obtain in the $t\to\infty$ limit a shuffle presentation of thequantum $Q$-system relations.

(t,q) Q-systems, DAHA and quantum toroidal algebras via generalized Macdonald operators