Vol. 12, No. 1, 2011

Download this article
Download this article For screen
For printing
Recent Issues
Volume 17, Issue 2
Volume 17, Issue 1
Volume 16, Issue 1
Volume 15, Issue 1
Volume 14, Issue 1
Volume 13, Issue 1
Volume 12, Issue 1
Volume 11, Issue 1
Volume 10, Issue 1
Volume 9, Issue 1
Volume 8, Issue 1
Volume 6+7, Issue 1
Volume 5, Issue 1
Volume 4, Issue 1
Volume 3, Issue 1
Volume 2, Issue 1
Volume 1, Issue 1
The Journal
About the Journal
Subscriptions
Editorial Board
Submission Guidelines
Submission Form
Ethics Statement
To Appear
Editorial Login
Contacts
ISSN (electronic): 2640-7345
ISSN (print): 2640-7337
Other MSP Journals
Maximal Levi subgroups acting on the Euclidean building of $\mathrm{GL}_n(F)$

Jonathan Needleman

Vol. 12 (2011), No. 1, 7–19
Abstract

In this paper we give a complete invariant of the action of GLn(F) × GLm(F) on the Euclidean building BGLn+m(F), where F is a discrete valuation field. We then use this invariant to give a natural metric on the resulting quotient space. In the special case of the torus acting on the tree BGL2(F), we obtain an algorithm for calculating the distance of any vertex in the tree to any fixed apartment.

Keywords
affine building, Euclidean building, Levi subgroup, group action
Mathematical Subject Classification 2010
Primary: 20E42, 20G25
Milestones
Received: 26 August 2009
Accepted: 19 May 2011
Authors
Jonathan Needleman