Loop groups
Arun Ram
Department of Mathematics
University of Wisconsin, Madison
Madison, WI 53706 USA
Last updates: 24 June 2007.
This page is the result of joint work with James Parkinson and
Christoph Schwer.
Loop groups and the Iwahori subgroup
A common setup is where is the field of fractions of , the discrete valuation ring is the ring of integers in , is the unique maximal ideal in , and is the residue field. The favourite examples are
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where is the field of -adic numbers, is the ring of -adic integers, and is the finite field with elements. The diagram
gives |
where
.
Then is the Iwahori subgroup of ,
- is the flag variety,
- is the affine flag variety, and
- is the loop Grassmanian.
Let
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Then
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so that .
Then
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and
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