Geometric methods for affine Deligne Lusztig varieties
Groups acting on CAT(0) spaces September 27, 2016 - September 30, 2016
Location: MSRI: Simons Auditorium
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
57-XX - Manifolds and cell complexes {For complex manifolds, see 32Qxx}
58D05 - Groups of diffeomorphisms and homeomorphisms as manifolds [See also 22E65, 57S05]
20F55 - Reflection and Coxeter groups [See also 22E40, 51F15]
20F70 - Algebraic geometry over groups; equations over groups
14609
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.
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14609
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