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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The $t=0$ specialization of the Mimachi-Noumi Cauchy-type identity rewritescertain infinite product in terms of specialized nonsymmetric Macdonaldpolynomials of type $GL_n$. We interpret the infinite product as a character ofthe space of functions on a certain matrix space. We show that the space offunctions admits a filtration such that the graded pieces are isomorphic to thetensor products of certain generalized global Weyl modules of the Iwahorialgebra. We identify the characters of the graded pieces with the terms of thespecialized Mimachi-Noumi formula. We conjecture the existence of an analogousfiltration on the space of functions on the Iwahori group for all simple Liealgebras and prove the conjecture for $SL_n$. Our construction can be seen as acurrent algebra extension of the van der Kallen filtration on functions on aBorel subgroup.

Nonsymmetric $q$-Cauchy identity and representations of the Iwahori algebra