Robinson-Schensted algorithms for Lie groups
Institue for Advanced Study
refreshments at 3:45pm
This talk will survey some combinatorial algorithms that arise
in the representation theory of Lie groups. Roughly speaking, given any
real Lie group $G$ two such algorithms emerge --- one from the structure
of `good' bases for certain Hecke algebra representations, and the other
from the structure of the canonical bases of Springer representations.
When $G = GL(n,\C)$, they both reduce to the classical Robinson-Schensted
algorithm. The point of this talk is to remove the ponderous
representation theoretic baggage from these algorithms, and instead
concentrate on their combinatorics. One combinatorial consequence is an
interesting partition of the group of $r$-signed permutations into
disjoint subsets. When $r=1$ or $2$, the partition recovers the
(weighted) Kazhdan-Lusztig cells for types A and BC.
Speaker's Contact Info: ptrapa(at-sign)math.mit.edu
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