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Friday, March 28, 2014 — 3:30 PM EDT

The Gindikin-Karpelevich Formula and Combinatorics of Crystals

Speaker: Jintai Ding
Affiliation: University of Cincinnati
Room: Mathematics and Computer Building (MC) 5168

Abstract:

The Gindikin-Karpelevich formula computes the constant of proportionality for the intertwining integral between two induced spherical representation of a $p$-adic reductive group $G.$ The right-hand side of this formula is a product over positive roots (with respect to the Langlands dual of $G$) which may also be interpreted as a sum over a crystal graph. The original interpretation as a sum is due to Brubaker-Bump-Friedberg and Bump-Nakasuji where $G=GL_{r+1},$  in  which  vertices  of the crystal graph are parametrized by paths to a specific vector in the graph according to a pattern prescribed by a reduced expression of the longest element of the Weyl group of $G$. I will explain this rule, explain how it may be translated into a statistic on the Young tableaux realization of the same crystal graph, and discuss its generalization to the affine Kac-Moody setting where the notion of the longest element of the Weyl group no longer makes sense.
 
This is joint work with Kyu-Hwan Lee, Seok-Jin Kang, and Hansol Ryu.

Location 
MC - Mathematics & Computer Building
5158
200 University Avenue West

Waterloo, ON N2L 3G1
Canada

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