Remarks on quantum unipotent subgroup and dual canonical basis

Yoshiyuki Kimura

doi:10.2140/pjm.2017.286.125

Home/Archive/arXiv

arXiv · 1506.07912

Remarks on quantum unipotent subgroup and dual canonical basis

Yoshiyuki Kimura

View original source ↗Read source document ↗Export metadata ↓

Abstract

We prove the tensor product decomposition of the half of quantized universal enveloping algebra associated with a Weyl group element which was conjectured by Berenstein and Greenstein.

Explore related subjects

math.QA math.RT

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Yoshiyuki Kimura. 2015-06-25. Remarks on quantum unipotent subgroup and dual canonical basis. https://doi.org/10.2140/pjm.2017.286.125

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Categorification of quasi-split iquantum groups

We introduce a new family of graded 2-categories generalizing the 2-quantum groups introduced by Khovanov, Lauda and Rouquier. We use them to categorify quasi-split iquantum groups in all symmetric types.

math.QA↗

arXiv2026

The Ring of Differential Operators on a Nodal Curve is not a Bialgebroid

In a previous article, we showed that local projectivity is a sufficient condition for the existence of a bialgebroid structure on the ring of differential operators on an affine variety. In this note, we show using elementary methods that the ring of differential operators on a nodal curve is neither locally projective nor does it admit a bialgebroid structure.

math.QA↗

arXiv2026

Coset representatives corresponding to Yetter-Drinfeld modules of modular group and continued fraction

We give complete conjugacy classes of modular group SL(2,Z). Particularly, the conjugacy classes of hyperbolic elements are decided by the proper equivalence classes of indefinite forms, and we give an example. Finally, we describe the coset representatives of centralizer of S, ST, T and hyperbolic elements of SL(2,Z) by regular continued fraction. In conclusion, most Nichols algebras over modular group are infinite-dimensional except Proposition 4.10.

math.QA↗