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/

Global: Zendy Plus annual

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

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We use the double affine Hecke algebra of type GL_N to construct an explicitconsistent system of q-difference equations, which we call the bispectralquantum Knizhnik-Zamolodchikov (BqKZ) equations. BqKZ includes, besidesCherednik's quantum affine KZ equations associated to principal seriesrepresentations of the underlying affine Hecke algebra, a compatible system ofq-difference equations acting on the central character of the principal seriesrepresentations. We construct a meromorphic self-dual solution \Phi of BqKZwhich, upon suitable specializations of the central character, reduces tosymmetric self-dual Laurent polynomial solutions of quantum KZ equations. Wegive an explicit correspondence between solutions of BqKZ and solutions of aparticular bispectral problem for the Ruijsenaars' commuting trigonometricq-difference operators. Under this correspondence \Phi becomes a self-dualHarish-Chandra series solution \Phi^+ of the bispectral problem. Specializingthe central character as above, we recover from \Phi^+ the symmetric self-dualMacdonald polynomials.

Double affine Hecke algebras and bispectral quantum Knizhnik-Zamolodchikov equations