Vol. 296, No. 1, 2018

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 297: 1
Vol. 296: 1  2
Vol. 295: 1  2
Vol. 294: 1  2
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
On the structure of cyclotomic nilHecke algebras

Jun Hu and Xinfeng Liang

Vol. 296 (2018), No. 1, 105–139
Abstract

In this paper we study the structure of the cyclotomic nilHecke algebras ,n(0), where ,n . We construct a monomial basis for ,n(0) which verifies a conjecture of Mathas. We show that the graded basic algebra of ,n(0) is commutative and hence isomorphic to the center Z of ,n(0). We further prove that ,n(0) is isomorphic to the full matrix algebra over Z and construct an explicit basis for the center Z. We also construct a complete set of pairwise orthogonal primitive idempotents of ,n(0). Finally, we present a new homogeneous symmetrizing form Tr on ,n(0) by explicitly specifying its values on a given homogeneous basis of ,n(0) and show that it coincides with Shan–Varagnolo–Vasserot’s symmetrizing form TrSVV on ,n(0).

Keywords
cyclotomic nilHecke algebras, graded cellular bases, trace forms
Mathematical Subject Classification 2010
Primary: 16G99, 20C08
Milestones
Received: 8 September 2017
Revised: 12 December 2017
Accepted: 20 December 2017
Published: 1 May 2018
Authors
Jun Hu
School of Mathematics and Statistics
Beijing Institute of Technology
Beijing
China
Xinfeng Liang
School of Mathematics and Statistics
Beijing Institute of Technology
Beijing
China