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Geometric methods for affine Deligne Lusztig varieties

Groups acting on CAT(0) spaces September 27, 2016 - September 30, 2016

September 27, 2016 (02:00 PM PDT - 02:50 PM PDT)
Speaker(s): Petra Schwer (Ruprecht-Karls-Universität Heidelberg)
Location: SLMath: Eisenbud Auditorium
Tags/Keywords

  • CAT(0) space

  • Algebraic groups

  • buildings and complexes

  • Coxeter groups

  • Deligne-Lusztig theory

  • Deligne-Lusztig variety

  • Iwahori subgroup

  • algebraic combinatorics

  • root lattice

  • Weyl group and chamber

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

14609
Abstract

Affine Deligne Lusztig varieties (ADLVs) are certain algebraic varieties associated to semisimple algebraic groups which have a Bruhat-Tits-building. We will explain how the geometry and combinatorics of the fundamental apartment of the building can be used to study nonemptiness and dimensions of ADLVs. Eventually all can be reduced to show existence and study the behaviour of certain positively folded galleries in affine Coxeter complexes.

Finally we will explain how one can obtain from nonemptiness and dimensions of ADLVs new insight on reflection length of elements of affine Coxeter groups.

This is joint work with Liz Milicevic and Anne Thomas.
Supplements
26811?type=thumb Schwer.Notes 2.17 MB application/pdf Download
Video/Audio Files

14609

H.264 Video 14609.mp4 285 MB video/mp4 rtsp://videos.msri.org/14609/14609.mp4 Download
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