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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Chinta and Gunnells introduced a rather intricate multi-parameter Weyl groupaction on rational functions on a torus, which, when the parameters arespecialized to certain Gauss sums, describes the functional equations of Weylgroup multiple Dirichlet series associated to metaplectic (n-fold) covers ofalgebraic groups. In subsequent joint work with Puskas, they extended thisaction to a "metaplectic" representation of the equal parameter affine Heckealgebra, which allowed them to obtain explicit formulas for the p-parts ofthese Dirichlet series. They have also verified by a computer check theremarkable fact that their formulas continue to define a group action forgeneral (unspecialized) parameters.  In the first part of paper we give a conceptual explanation of this fact, bygiving a uniform and elementary construction of the "metaplectic"representation for generic Hecke algebras as a suitable quotient of aparabolically induced affine Hecke algebra module, from which the associatedChinta-Gunnells Weyl group action follows through localization.  In the second part of the paper we extend the metaplectic representation tothe double affine Hecke algebra, which provides a generalization of Cherednik'sbasic representation. This allows us to introduce a new family of "metaplectic"polynomials, which generalize nonsymmetric Macdonald polynomials. In thispaper, we provide the details of the construction of metaplectic polynomials intype A; the general case will be handled in the sequel to this paper.

Metaplectic representations of Hecke algebras, Weyl group actions, and associated polynomials