Vol. 8, No. 4, 2014

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 9, 1845–2052
Issue 8, 1601–1843
Issue 7, 1373–1600
Issue 6, 1147–1371
Issue 5, 939–1146
Issue 4, 695–938
Issue 3, 451–694
Issue 2, 215–450
Issue 1, 1–214

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
Cover
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Yangians and quantizations of slices in the affine Grassmannian

Joel Kamnitzer, Ben Webster, Alex Weekes and Oded Yacobi

Vol. 8 (2014), No. 4, 857–893
Abstract

We study quantizations of transverse slices to Schubert varieties in the affine Grassmannian. The quantization is constructed using quantum groups called shifted Yangians — these are subalgebras of the Yangian we introduce which generalize the Brundan–Kleshchev shifted Yangian to arbitrary type. Building on ideas of Gerasimov, Kharchev, Lebedev and Oblezin, we prove that a quotient of the shifted Yangian quantizes a scheme supported on the transverse slices, and we formulate a conjectural description of the defining ideal of these slices which implies that the scheme is reduced. This conjecture also implies the conjectural quantization of the Zastava spaces for PGLn of Finkelberg and Rybnikov.

Keywords
quantization, affine Grassmannian, quantum groups, Yangian
Mathematical Subject Classification 2010
Primary: 20G42
Secondary: 53D55, 14M15, 14D24
Milestones
Received: 10 January 2013
Revised: 2 August 2013
Accepted: 31 August 2013
Published: 10 August 2014
Authors
Joel Kamnitzer
Department of Mathematics
University of Toronto
40 St. George Street
Toronto, ON M5S 2E4
Canada
Ben Webster
Department of Mathematics
University of Virginia
141 Cabell Drive
Charlottesville, VA 22904
United States
Alex Weekes
Department of Mathematics
University of Toronto
40 St. George Street
Toronto, ON M5S 2E4
Canada
Oded Yacobi
School of Mathematics and Statistics
University of Sydney
NSW 2006
Australia