表現論セミナー Burge 対応とCrystal Structure（菊池 啓）

菊池 啓氏 (北海道大学)

We focus on the relationship between semistandard tableaux and

crystal structures.

While the Robinson-Schensted-Knuth (RSK) correspondence is well-known as a

correspondence between semistandard tableaux and two-rowed arrays,

we consider a further restriction on such two-rowed arrays, called

Burge arrays.

We then define readings and the actions of Kashiwara operators on

semistandard tableaux and Burge arrays.

Moreover, we impose a condition called PV-free on Burge arrays. This

condition characterizes the shape of a semistandard tableau obtained from a

Burge array.

As a result, the set of PV-free Burge arrays admits a crystal structure.