Description
It is known that the quantum coordinate algebra of a Kac--Moody algebra and its crystal basis admit Peter--Weyl type decompositions.
Also, Kashiwara proved that, for finite type, the crystal basis is isomorphic to the crystal basis of the modified quantum group as bicrystals.
The main topic of this talk is quantum symmetric pair analogues of these results.
In particular, I will show you some examples of "bi-icrystals" of type A.
This talk is partly based on a joint work with Mao Hoshino.
Author
Hideya Watanabe
(Rikkyo University)