Vol. 255, No. 2, 2012

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 311: 1
Vol. 310: 1  2
Vol. 309: 1  2
Vol. 308: 1  2
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
Quantum affine algebras, canonical bases, and q-deformation of arithmetical functions

Henry H. Kim and Kyu-Hwan Lee

Vol. 255 (2012), No. 2, 393–415
Abstract

We obtain affine analogs of the Gindikin–Karpelevich and Casselman–Shalika formulas as sums over Kashiwara and Lusztig’s canonical bases. As suggested by these formulas, we define natural q-deformation of arithmetical functions such as (multi)partition functions and Ramanujan τ-functions, and prove various identities among them. In some examples we recover classical identities by taking limits. Additionally, we consider q-deformation of the Kostant function and study certain q-polynomials whose special values are weight multiplicities.

Keywords
quantum affine algebras, canonical bases, q-deformation of arithmetic functions
Mathematical Subject Classification 2010
Primary: 17B37
Secondary: 05E10
Milestones
Received: 24 January 2011
Accepted: 7 June 2011
Published: 10 April 2012
Authors
Henry H. Kim
Department of Mathematics
University of Toronto
Toronto, Ontario M5S2E4
Canada
Korea Institute for Advanced Study
Seoul
Korea
Kyu-Hwan Lee
Department of Mathematics
University of Connecticut
Storrs, CT 06269-3009
United States