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1. The algebraic story
1. The algebraic story
2. Relation to W-algebras
Answer: (McDowell)
Example:
e-actionf-actionh-action
...
2
0
-2
-4
2
1
-1
1
2
3
4
Case 1: completely degenerate
Case 2: non-degenerate
Verma module!
The second natural question:
2. Relation to W-algebras
2. Relation to W-algebras
3. The geometric story
3. The geometric story
3. The geometric story
3. The geometric story
Set-up:
example:
A remarkable bridge:
Twisted Harish-Chandra sheaves:
Example:
C(w)
X=
open Bruhat cell=
Choose
4. The algorithm
4. The algorithm
4. The algorithm
3
1
2
3
4
3
3
3
1
1
1
1
Set-up:
Relating Deodar's theorem to D-modules:
The punchline:
These are holonomic D-moduleswith irregular singularities
So the polynomials in Deodhar's algorithm compute composition multiplicities of Whittaker modules!
Thank you!