### KR crystals and combinatorial R-matrices

Okado, M *(Osaka)*

Tuesday 31 March 2009, 14:15-15:00

Satellite

#### Abstract

Recently the existence of crystal bases for KR modules was shown for all nonexceptional ane types and their combinatorial structures were claried. Our next problem is to calculate the image of the combinatorial R-matrix for any pair of KR crystals. As a rst step, we calculate it for any classical highest weight element in the tensor product of KR crystals Br;k
B1;l for type D(1) n ;B(1) n ;A(2) 2n..1.
The notion of -diagrams is eectively used for the identication of classical highest weight elements in B1;l
Br;k. This is a joint work with Reiho Sakamoto.

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