Robinson-Schensted algorithms for Lie groups

Peter Trapa

Institue for Advanced Study

November 13,
4:15pm
refreshments at 3:45pm
2-338

ABSTRACT 

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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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)math.mit.edu

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