arxiv:2601.00524

iQuantum groups and iHopf algebras II: dual canonical bases

Published on Jan 2

Authors:

Abstract

Building on the iHopf algebra realization of quasi-split universal iquantum groups developed in a prequel, we construct the dual canonical basis for a universal iquantum group of arbitrary finite type, which are further shown to be preserved by the ibraid group action; this recovers the results of Lu-Pan in ADE type obtained earlier in a geometric approach. Moreover, we identify the dual canonical basis for the Drinfeld double quantum group of arbitrary finite type, which is realized via iHopf algebra on the double Borel, with Berenstein-Greenstein's double canonical basis, settling several of their conjectures.

View arXiv page View PDF Add to collection

Community

Upload images, audio, and videos by dragging in the text input, pasting, or clicking here.

Tap or paste here to upload images

· Sign up or log in to comment

Upvote

Models citing this paper 0

No model linking this paper

Cite arxiv.org/abs/2601.00524 in a model README.md to link it from this page.

Datasets citing this paper 0

No dataset linking this paper

Cite arxiv.org/abs/2601.00524 in a dataset README.md to link it from this page.

Spaces citing this paper 0

No Space linking this paper

Cite arxiv.org/abs/2601.00524 in a Space README.md to link it from this page.

Collections including this paper 0

No Collection including this paper

Add this paper to a collection to link it from this page.